{"categories":["FX"],"contentHtml":"<h3>Week 5 — 24 February 2025</h3><p>The syllabus calls this class “Introduction to Black-Scholes. BS usage for a practitioner. First and Second order risks. Xgamma. Intuitive awareness.” The source notes are the VBA workbook below, so the article preserves the implementation rather than replacing it with a summary.</p><h4>Notes on inputs</h4><ul><li>(T = Days / 365)</li><li>(S = Forward) (the workbook expects forward FX)</li><li>(X = Strike)</li><li>(r = DiscRate)</li><li>(v = vol)</li><li>(ExtRate) is the foreign-currency rate.</li><li>All returned prices are in USD.</li></ul><h4>BSPrice</h4><p>This is a cleaned transcription of the source workbook function. The branches cover calls, puts, forwards, and the two zero-coupon deposits recorded in the notes.</p><pre><code>Function BSPrice(ContractType As String, _\n                 Forward As Double, _\n                 Strike As Double, _\n                 Days As Double, _\n                 DiscRate As Double, _\n                 ExtRate As Double, _\n                 vol As Double)\n    T = Days / 365\n    S = Forward\n    X = Strike\n    r = DiscRate\n    v = vol\n    OptionType = ContractType\n    ' Call Option\n    If OptionType = \"C\" Then\n        BSPrice = Exp(-r * T) * (S * Application.NormSDist(dOne(S, X, T, r, v)) - X * Application.NormSDist(dTwo(S, X, T, r, v)))\n    ' Put Option\n    ElseIf OptionType = \"P\" Then\n        BSPrice = Exp(-r * T) * (X * Application.NormSDist(-dTwo(S, X, T, r, v)) - S * Application.NormSDist(-dOne(S, X, T, r, v)))\n    ' Fwd FX\n    ElseIf OptionType = \"F\" Then\n        BSPrice = Exp(-r * T) * (S - X)\n    ' Deposit in USD (ZC in USD)\n    ElseIf OptionType = \"D\" Then\n        BSPrice = Exp(-r * T)\n    ' Deposit in MXN (ZCB in MXN)\n    ElseIf OptionType = \"M\" Then\n        BSPrice = Exp(-r * T) * S\n    End If\nEnd Function</code></pre>","contentSourceFormat":"typst","contentTypst":"== Week 5 --- 24 February 2025\n<week-5-24-february-2025>\nThe syllabus calls this class \"Introduction to Black-Scholes. BS usage for a practitioner. First and Second order risks. Xgamma. Intuitive awareness.\" The source notes are the VBA workbook below, so the article preserves the implementation rather than replacing it with a summary.\n\n=== Notes on inputs\n<notes-on-inputs>\n- \\(T = Days / 365)\n- \\(S = Forward) (the workbook expects forward FX)\n- \\(X = Strike)\n- \\(r = DiscRate)\n- \\(v = vol)\n- \\(ExtRate) is the foreign-currency rate.\n- All returned prices are in USD.\n\n=== BSPrice\n<bsprice>\nThis is a cleaned transcription of the source workbook function. The branches cover calls, puts, forwards, and the two zero-coupon deposits recorded in the notes.\n\n```vb\nFunction BSPrice(ContractType As String, _\n                 Forward As Double, _\n                 Strike As Double, _\n                 Days As Double, _\n                 DiscRate As Double, _\n                 ExtRate As Double, _\n                 vol As Double)\n    T = Days / 365\n    S = Forward\n    X = Strike\n    r = DiscRate\n    v = vol\n    OptionType = ContractType\n    ' Call Option\n    If OptionType = \"C\" Then\n        BSPrice = Exp(-r * T) * (S * Application.NormSDist(dOne(S, X, T, r, v)) - X * Application.NormSDist(dTwo(S, X, T, r, v)))\n    ' Put Option\n    ElseIf OptionType = \"P\" Then\n        BSPrice = Exp(-r * T) * (X * Application.NormSDist(-dTwo(S, X, T, r, v)) - S * Application.NormSDist(-dOne(S, X, T, r, v)))\n    ' Fwd FX\n    ElseIf OptionType = \"F\" Then\n        BSPrice = Exp(-r * T) * (S - X)\n    ' Deposit in USD (ZC in USD)\n    ElseIf OptionType = \"D\" Then\n        BSPrice = Exp(-r * T)\n    ' Deposit in MXN (ZCB in MXN)\n    ElseIf OptionType = \"M\" Then\n        BSPrice = Exp(-r * T) * S\n    End If\nEnd Function\n```","dataUrl":"https://sharifhsn.dev/api/posts/fx-black-scholes-pricing.json","date":"2025-02-24","datePublished":"2025-02-24","description":"The syllabus calls this class “Introduction to Black-Scholes. BS usage for a practitioner. First and Second order risks. Xgamma. Intuitive awareness.” The source notes are the…","site":"https://sharifhsn.dev","slug":"fx-black-scholes-pricing","source":"FE-635 | Risk Engineering","sourceUrl":null,"tags":["FX","Black–Scholes","Option Pricing"],"title":"Black–Scholes Pricing for FX","url":"https://sharifhsn.dev/blog/fx-black-scholes-pricing/","version":"1","wordCount":273}