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bsoption

The goal of this R package (bsoption) is to provide a quick platform for pricing index (and currency) exchange traded options. This also include a SABR and quadratic smile volatility calibration method. Also user can extract implied and realized distributions and use a given underlying distribution to price options for relative value analysis.

Installation

You can install bsoption from github with:

# install.packages("devtools")devtools::install_github("prodipta/bsoption")

Example

This is a basic example which shows you how to calibrate a SABR vol from market prices of options. The dataframe opt_chain is provided with the package:

?opt_chainsabrVol<- calibrate(opt_chain,as.Date("2017-07-11"),model="sabr")
quadVol<- calibrate(opt_chain,as.Date("2017-07-11"))
k<- seq(90,110,0.5)
vols1<- getVol(sabrVol,100,k)
vols2<- getVol(quadVol,100,k)
plot(k,vols1,type="n")
lines(k,vols1,col="red")
lines(k,vols2,col="blue")

Following example shows how to extract implied probability distribution and use that to price an option

voldist<- impliedDistribution(sabrVol)
plot(voldist$k,voldist$p,type="n")
lines(voldist$k,voldist$p,col="blue")
distributionPricer(100,101,voldist,type="call")

Following example shows how to exatract implied volatility and use the main pricing function to price options. These functions can handle fractional day pricing (the date argument should be in POSIX format in YYYY:MM:DD HH:MM).

vol<- bsImpliedVol(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),25.40,type="call")
bsPlainVanillaOption(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),vol ,type="call")

About

Package for option pricing and volatility calibration for index (and FX) options

Topics

option-pricingsabrvolatility

Resources

Readme
Activity

Stars

8 stars

Watchers

4 watching

Forks

4 forks
Report repository

Releases

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Contributors

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})();
(function(){
try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '

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bsoption
The goal of this R package (bsoption) is to provide a quick platform for pricing index (and currency) exchange traded options. This also include a SABR and quadratic smile volatility calibration method. Also user can extract implied and realized distributions and use a given underlying distribution to price options for relative value analysis.
Installation
You can install bsoption from github with:
# install.packages("devtools")devtools::install_github("prodipta/bsoption")
Example
This is a basic example which shows you how to calibrate a SABR vol from market prices of options. The dataframe opt_chain is provided with the package:
?opt_chainsabrVol<- calibrate(opt_chain,as.Date("2017-07-11"),model="sabr")
quadVol<- calibrate(opt_chain,as.Date("2017-07-11"))
k<- seq(90,110,0.5)
vols1<- getVol(sabrVol,100,k)
vols2<- getVol(quadVol,100,k)
plot(k,vols1,type="n")
lines(k,vols1,col="red")
lines(k,vols2,col="blue")
Following example shows how to extract implied probability distribution and use that to price an option
voldist<- impliedDistribution(sabrVol)
plot(voldist$k,voldist$p,type="n")
lines(voldist$k,voldist$p,col="blue")
distributionPricer(100,101,voldist,type="call")
Following example shows how to exatract implied volatility and use the main pricing function to price options. These functions can handle fractional day pricing (the date argument should be in POSIX format in YYYY:MM:DD HH:MM).
vol<- bsImpliedVol(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),25.40,type="call")
bsPlainVanillaOption(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),vol ,type="call")
About
Package for option pricing and volatility calibration for index (and FX) options
Topics
option-pricingsabrvolatility
Resources
Readme
Activity
Stars
8 stars
Watchers
4 watching
Forks
4 forks
Report repository
Releases
Packages
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Force GitHub README to respect dark mode\n(function() {\n var style = document.createElement('style');\n style.textContent = '\n .markdown-body {\n color-scheme: dark light;\n }\n .markdown-body pre { background: #161b22 !important; }\n .markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }\n .markdown-body table th, .markdown-body table td { border-color: #30363d !important; }\n .markdown-body img { background: #0d1117; }\n .markdown-body blockquote { border-left-color: #8b949e; }\n .markdown-body hr { border-color: #30363d; }\n ';\n document.head.appendChild(style);\n})();", "GitHub Dark Mode README Fix");
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} catch(__e) { console.warn('[Userscript:GitHub Dark Mode README Fix]', __e); }
})();
(function(){
try {
var __m = "*";
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bsoption
The goal of this R package (bsoption) is to provide a quick platform for pricing index (and currency) exchange traded options. This also include a SABR and quadratic smile volatility calibration method. Also user can extract implied and realized distributions and use a given underlying distribution to price options for relative value analysis.
Installation
You can install bsoption from github with:
# install.packages("devtools")devtools::install_github("prodipta/bsoption")
Example
This is a basic example which shows you how to calibrate a SABR vol from market prices of options. The dataframe opt_chain is provided with the package:
?opt_chainsabrVol<- calibrate(opt_chain,as.Date("2017-07-11"),model="sabr")
quadVol<- calibrate(opt_chain,as.Date("2017-07-11"))
k<- seq(90,110,0.5)
vols1<- getVol(sabrVol,100,k)
vols2<- getVol(quadVol,100,k)
plot(k,vols1,type="n")
lines(k,vols1,col="red")
lines(k,vols2,col="blue")
Following example shows how to extract implied probability distribution and use that to price an option
voldist<- impliedDistribution(sabrVol)
plot(voldist$k,voldist$p,type="n")
lines(voldist$k,voldist$p,col="blue")
distributionPricer(100,101,voldist,type="call")
Following example shows how to exatract implied volatility and use the main pricing function to price options. These functions can handle fractional day pricing (the date argument should be in POSIX format in YYYY:MM:DD HH:MM).
vol<- bsImpliedVol(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),25.40,type="call")
bsPlainVanillaOption(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),vol ,type="call")
About
Package for option pricing and volatility calibration for index (and FX) options
Topics
option-pricingsabrvolatility
Resources
Readme
Activity
Stars
8 stars
Watchers
4 watching
Forks
4 forks
Report repository
Releases
Packages
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Highlight search terms from Google/DuckDuckGo/Bing referrer\n(function() {\n var ref = document.referrer;\n var terms = [];\n \n if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {\n var url = new URL(ref);\n var q = url.searchParams.get('q') || url.searchParams.get('p');\n if (q) {\n terms = q.split(/\\s+/).filter(function(t) { return t.length > 2; });\n }\n }\n \n if (terms.length === 0) return;\n \n var style = document.createElement('style');\n style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';\n document.head.appendChild(style);\n \n function highlight(node) {\n if (node.nodeType === 3) { // text node\n var text = node.textContent;\n var found = false;\n terms.forEach(function(term) {\n var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\\]\\\\]/g, '\\\\') + ')', 'gi');\n if (regex.test(text)) {\n found = true;\n var frag = document.createDocumentFragment();\n var parts = text.split(regex);\n parts.forEach(function(part, i) {\n if (i % 2 === 0) {\n frag.appendChild(document.createTextNode(part));\n } else {\n var span = document.createElement('span');\n span.className = 'userscript-highlight';\n span.textContent = part;\n frag.appendChild(span);\n }\n });\n node.parentNode.replaceChild(frag, node);\n }\n });\n } else if (node.nodeType === 1 && node.childNodes) { // element\n var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];\n if (!skipTags.includes(node.tagName)) {\n Array.from(node.childNodes).forEach(highlight);\n }\n }\n }\n \n highlight(document.body);\n \n // Re-highlight on dynamic content\n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1 || node.nodeType === 3) highlight(node);\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Highlight Search Terms");
}
} catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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bsoption
The goal of this R package (bsoption) is to provide a quick platform for pricing index (and currency) exchange traded options. This also include a SABR and quadratic smile volatility calibration method. Also user can extract implied and realized distributions and use a given underlying distribution to price options for relative value analysis.
Installation
You can install bsoption from github with:
# install.packages("devtools")devtools::install_github("prodipta/bsoption")
Example
This is a basic example which shows you how to calibrate a SABR vol from market prices of options. The dataframe opt_chain is provided with the package:
?opt_chainsabrVol<- calibrate(opt_chain,as.Date("2017-07-11"),model="sabr")
quadVol<- calibrate(opt_chain,as.Date("2017-07-11"))
k<- seq(90,110,0.5)
vols1<- getVol(sabrVol,100,k)
vols2<- getVol(quadVol,100,k)
plot(k,vols1,type="n")
lines(k,vols1,col="red")
lines(k,vols2,col="blue")
Following example shows how to extract implied probability distribution and use that to price an option
voldist<- impliedDistribution(sabrVol)
plot(voldist$k,voldist$p,type="n")
lines(voldist$k,voldist$p,col="blue")
distributionPricer(100,101,voldist,type="call")
Following example shows how to exatract implied volatility and use the main pricing function to price options. These functions can handle fractional day pricing (the date argument should be in POSIX format in YYYY:MM:DD HH:MM).
vol<- bsImpliedVol(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),25.40,type="call")
bsPlainVanillaOption(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),vol ,type="call")
About
Package for option pricing and volatility calibration for index (and FX) options
Topics
option-pricingsabrvolatility
Resources
Readme
Activity
Stars
8 stars
Watchers
4 watching
Forks
4 forks
Report repository
Releases
Packages
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Strip utm_, fbclid, gclid, etc. from all links on page\n(function() {\n var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',\n 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',\n 'ref', 'ref_src', 'source', 'medium', 'campaign'];\n \n function cleanUrl(url) {\n try {\n var u = new URL(url, window.location.origin);\n var changed = false;\n trackingParams.forEach(function(p) {\n if (u.searchParams.has(p)) {\n u.searchParams.delete(p);\n changed = true;\n }\n });\n return changed ? u.toString() : url;\n } catch (e) {\n return url;\n }\n }\n \n function cleanLinks() {\n document.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n \n cleanLinks();\n \n var observer = new MutationObserver(function(mutations) {\n mutations.forEach(function(m) {\n m.addedNodes.forEach(function(node) {\n if (node.nodeType === 1) {\n if (node.tagName === 'A') cleanLinks();\n node.querySelectorAll('a[href]').forEach(function(a) {\n var clean = cleanUrl(a.href);\n if (clean !== a.href) a.href = clean;\n });\n }\n });\n });\n });\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Remove Tracking Parameters from Links");
}
} catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); }
})();
(function(){
try {
var __m = "youtube.com";
var __re = new RegExp('^' + "youtube\\.com" + '

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bsoption
The goal of this R package (bsoption) is to provide a quick platform for pricing index (and currency) exchange traded options. This also include a SABR and quadratic smile volatility calibration method. Also user can extract implied and realized distributions and use a given underlying distribution to price options for relative value analysis.
Installation
You can install bsoption from github with:
# install.packages("devtools")devtools::install_github("prodipta/bsoption")
Example
This is a basic example which shows you how to calibrate a SABR vol from market prices of options. The dataframe opt_chain is provided with the package:
?opt_chainsabrVol<- calibrate(opt_chain,as.Date("2017-07-11"),model="sabr")
quadVol<- calibrate(opt_chain,as.Date("2017-07-11"))
k<- seq(90,110,0.5)
vols1<- getVol(sabrVol,100,k)
vols2<- getVol(quadVol,100,k)
plot(k,vols1,type="n")
lines(k,vols1,col="red")
lines(k,vols2,col="blue")
Following example shows how to extract implied probability distribution and use that to price an option
voldist<- impliedDistribution(sabrVol)
plot(voldist$k,voldist$p,type="n")
lines(voldist$k,voldist$p,col="blue")
distributionPricer(100,101,voldist,type="call")
Following example shows how to exatract implied volatility and use the main pricing function to price options. These functions can handle fractional day pricing (the date argument should be in POSIX format in YYYY:MM:DD HH:MM).
vol<- bsImpliedVol(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),25.40,type="call")
bsPlainVanillaOption(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),vol ,type="call")
About
Package for option pricing and volatility calibration for index (and FX) options
Topics
option-pricingsabrvolatility
Resources
Readme
Activity
Stars
8 stars
Watchers
4 watching
Forks
4 forks
Report repository
Releases
Packages
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Auto-enable theater mode on YouTube\n(function() {\n function tryTheater() {\n var btn = document.querySelector('button[aria-label=\"Theater mode\"], ytd-player #player button[title=\"Theater mode\"]');\n if (btn && !btn.classList.contains('activated')) {\n btn.click();\n }\n }\n \n // Try immediately\n tryTheater();\n \n // Try after navigation (SPA)\n var lastUrl = location.href;\n setInterval(function() {\n if (location.href !== lastUrl) {\n lastUrl = location.href;\n setTimeout(tryTheater, 500);\n }\n }, 1000);\n \n // Also try on player load\n var observer = new MutationObserver(tryTheater);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "YouTube Theater Mode Default");
}
} catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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bsoption
The goal of this R package (bsoption) is to provide a quick platform for pricing index (and currency) exchange traded options. This also include a SABR and quadratic smile volatility calibration method. Also user can extract implied and realized distributions and use a given underlying distribution to price options for relative value analysis.
Installation
You can install bsoption from github with:
# install.packages("devtools")devtools::install_github("prodipta/bsoption")
Example
This is a basic example which shows you how to calibrate a SABR vol from market prices of options. The dataframe opt_chain is provided with the package:
?opt_chainsabrVol<- calibrate(opt_chain,as.Date("2017-07-11"),model="sabr")
quadVol<- calibrate(opt_chain,as.Date("2017-07-11"))
k<- seq(90,110,0.5)
vols1<- getVol(sabrVol,100,k)
vols2<- getVol(quadVol,100,k)
plot(k,vols1,type="n")
lines(k,vols1,col="red")
lines(k,vols2,col="blue")
Following example shows how to extract implied probability distribution and use that to price an option
voldist<- impliedDistribution(sabrVol)
plot(voldist$k,voldist$p,type="n")
lines(voldist$k,voldist$p,col="blue")
distributionPricer(100,101,voldist,type="call")
Following example shows how to exatract implied volatility and use the main pricing function to price options. These functions can handle fractional day pricing (the date argument should be in POSIX format in YYYY:MM:DD HH:MM).
vol<- bsImpliedVol(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),25.40,type="call")
bsPlainVanillaOption(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),vol ,type="call")
About
Package for option pricing and volatility calibration for index (and FX) options
Topics
option-pricingsabrvolatility
Resources
Readme
Activity
Stars
8 stars
Watchers
4 watching
Forks
4 forks
Report repository
Releases
Packages
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Remove or un-stick sticky/fixed headers that block content\n(function() {\n function unstick() {\n document.querySelectorAll('header, nav, [role=\"banner\"], .header, .navbar, .sticky, .fixed-top, [style*=\"position: fixed\"], [style*=\"position:sticky\"]').forEach(function(el) {\n if (el.style.position === 'fixed' || el.style.position === 'sticky' || \n getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {\n el.style.position = 'static';\n el.style.top = 'auto';\n el.style.zIndex = 'auto';\n }\n });\n }\n \n unstick();\n \n var observer = new MutationObserver(unstick);\n observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });\n})();", "Kill Sticky Headers");
}
} catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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bsoption
The goal of this R package (bsoption) is to provide a quick platform for pricing index (and currency) exchange traded options. This also include a SABR and quadratic smile volatility calibration method. Also user can extract implied and realized distributions and use a given underlying distribution to price options for relative value analysis.
Installation
You can install bsoption from github with:
# install.packages("devtools")devtools::install_github("prodipta/bsoption")
Example
This is a basic example which shows you how to calibrate a SABR vol from market prices of options. The dataframe opt_chain is provided with the package:
?opt_chainsabrVol<- calibrate(opt_chain,as.Date("2017-07-11"),model="sabr")
quadVol<- calibrate(opt_chain,as.Date("2017-07-11"))
k<- seq(90,110,0.5)
vols1<- getVol(sabrVol,100,k)
vols2<- getVol(quadVol,100,k)
plot(k,vols1,type="n")
lines(k,vols1,col="red")
lines(k,vols2,col="blue")
Following example shows how to extract implied probability distribution and use that to price an option
voldist<- impliedDistribution(sabrVol)
plot(voldist$k,voldist$p,type="n")
lines(voldist$k,voldist$p,col="blue")
distributionPricer(100,101,voldist,type="call")
Following example shows how to exatract implied volatility and use the main pricing function to price options. These functions can handle fractional day pricing (the date argument should be in POSIX format in YYYY:MM:DD HH:MM).
vol<- bsImpliedVol(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),25.40,type="call")
bsPlainVanillaOption(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),vol ,type="call")
About
Package for option pricing and volatility calibration for index (and FX) options
Topics
option-pricingsabrvolatility
Resources
Readme
Activity
Stars
8 stars
Watchers
4 watching
Forks
4 forks
Report repository
Releases
Packages
Contributors
Languages

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Universal Dark Mode - works on any site\n(function() {\n var enabled = true;\n \n function applyDarkMode() {\n if (!enabled) return;\n \n // Create style element if it doesn't exist\n var style = document.getElementById('universal-dark-mode-style');\n if (!style) {\n style = document.createElement('style');\n style.id = 'universal-dark-mode-style';\n document.head.appendChild(style);\n }\n \n // Dark mode CSS - inverts colors but preserves images/video\n style.textContent = '\n /* Invert everything except media */\n html {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #1a1a2e !important;\n }\n \n /* Restore images, videos, iframes, canvas */\n img, video, iframe, canvas, svg, picture, [style*=\"background-image\"] {\n filter: invert(1) hue-rotate(180deg) !important;\n }\n \n /* Preserve specific elements that should not be inverted */\n .no-dark-mode, .no-dark-mode *,\n [data-theme=\"light\"], [data-theme=\"light\"],\n .ace_editor, .ace_editor *,\n .CodeMirror, .CodeMirror *,\n .monaco-editor, .monaco-editor *,\n .markdown-body pre, .markdown-body pre *,\n .highlight, .highlight *,\n pre code, pre code * {\n filter: none !important;\n }\n \n /* Fix common UI elements */\n .modal, .popup, .dropdown-menu, .tooltip, .popover {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #2d2d44 !important;\n border-color: #444 !important;\n }\n \n /* Scrollbars */\n ::-webkit-scrollbar { background: #1a1a2e !important; }\n ::-webkit-scrollbar-thumb { background: #444 !important; }\n ::-webkit-scrollbar-thumb:hover { background: #555 !important; }\n \n /* Selection */\n ::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ';\n }\n \n function removeDarkMode() {\n var style = document.getElementById('universal-dark-mode-style');\n if (style) style.remove();\n }\n \n // Toggle with Alt+Shift+D\n document.addEventListener('keydown', function(e) {\n if (e.altKey && e.shiftKey && e.key === 'D') {\n e.preventDefault();\n enabled = !enabled;\n if (enabled) {\n applyDarkMode();\n console.log('[Universal Dark Mode] Enabled');\n } else {\n removeDarkMode();\n console.log('[Universal Dark Mode] Disabled');\n }\n }\n });\n \n // Apply on load\n applyDarkMode();\n \n // Re-apply on dynamic content\n var observer = new MutationObserver(function(mutations) {\n if (enabled && !document.getElementById('universal-dark-mode-style')) {\n applyDarkMode();\n }\n });\n observer.observe(document.head, { childList: true });\n \n console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');\n})();", "Universal Dark Mode");
}
} catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); }
})();
})();

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bsoption
The goal of this R package (bsoption) is to provide a quick platform for pricing index (and currency) exchange traded options. This also include a SABR and quadratic smile volatility calibration method. Also user can extract implied and realized distributions and use a given underlying distribution to price options for relative value analysis.
Installation
You can install bsoption from github with:
# install.packages("devtools")devtools::install_github("prodipta/bsoption")
Example
This is a basic example which shows you how to calibrate a SABR vol from market prices of options. The dataframe opt_chain is provided with the package:
?opt_chainsabrVol<- calibrate(opt_chain,as.Date("2017-07-11"),model="sabr")
quadVol<- calibrate(opt_chain,as.Date("2017-07-11"))
k<- seq(90,110,0.5)
vols1<- getVol(sabrVol,100,k)
vols2<- getVol(quadVol,100,k)
plot(k,vols1,type="n")
lines(k,vols1,col="red")
lines(k,vols2,col="blue")
Following example shows how to extract implied probability distribution and use that to price an option
voldist<- impliedDistribution(sabrVol)
plot(voldist$k,voldist$p,type="n")
lines(voldist$k,voldist$p,col="blue")
distributionPricer(100,101,voldist,type="call")
Following example shows how to exatract implied volatility and use the main pricing function to price options. These functions can handle fractional day pricing (the date argument should be in POSIX format in YYYY:MM:DD HH:MM).
vol<- bsImpliedVol(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),25.40,type="call")
bsPlainVanillaOption(as.Date("2017-07-13"),9879.55,10000,as.Date("2017-07-27"),vol ,type="call")
About
Package for option pricing and volatility calibration for index (and FX) options
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option-pricingsabrvolatility
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