파생금융상품 실무 - EXCEL PRICING 실습 - 제일은행 자금부 과장 신 종 찬

2 Zero Coupon Yield Curve Construction with U$ Swap Rate (p.a.) U$ Market Information Today: Nov. 16, 2002 Spot date: Nov. 19, 2002 Swap day-count: xxx% p.a. Act/360 Market Rate Money MarketSwap Market O/N1.37%2Y2.24% 1W1.36%3Y2.77% 1M1.39%4Y3.16% 2M1.42%5Y3.48% 3M1.42%7Y4.00% 6M1.45%10Y4.51% 1Y1.65%

3 Zero Coupon Yield Curve Construction with U$ Swap Rate (p.a.)

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9 Zero Coupon Yield Curve Construction with GBP Swap Rate (s.a.) U$ Market Information Today: Nov. 16, 2002 Spot date: Nov. 18, 2002 Swap daycount: xxx% s.a. Act/365 Market Rate Money MarketSwap Market O/N3.42%2Y4.30% 1W3.78%3Y4.45% 1M3.95%4Y4.57% 2M3.97%5Y4.66% 3M3.99%7Y4.79% 6M4.02%10Y4.93% 1Y4.12%

10 Zero Coupon Yield Curve Construction with GBP Swap Rate (s.a.)

11 Swap & Cashflow Manager (Sample)

12 Swap & Cashflow Manager (Sample)

13 Swap & Cashflow Manager (Sample)

14 Currency Option Pricing Black-Scholes Pricing VBA Code Function EC(S, X, Sday, Mday, vol, r, rf) As Double Dim T As Double Dim d1 As Double Dim d2 As Double T = (Mday - Sday) / 365 d1 = (Log(S / X) + (r - rf + vol ^ 2 / 2) * T) / (vol * T ^ 0.5) d2 = d1 - vol * T ^ 0.5 EC = Exp(-rf * T) * S * Application.NormSDist(d1) - Exp(-r * T) * X * Application.NormSDist(d2) End Function Function EP(S, X, Sday, Mday, vol, r, rf) As Double Dim T As Double Dim d1 As Double Dim d2 As Double T = (Mday - Sday) / 365 d1 = (Log(S / X) + (r - rf + vol ^ 2 / 2) * T) / (vol * T ^ 0.5) d2 = d1 - vol * T ^ 0.5 EP = Exp(-r * T) * X * Application.NormSDist(-d2) - Exp(-rf * T) * S * Application.NormSDist(-d1) End Function

15 Currency Option Pricing Binomial European Option Pricing VBA Code Function Binomial_European(S, X, Sday, Mday, vol, r, rf, Call_Put, N) Dim St(0 To 200, 0 To 200) As Double Dim optlet_price(0 To 200, 0 To 200) As Double tau = (Mday - Sday) / 365 dt = tau / N u = Exp(vol * Sqr(dt)) d = 1 / u a = Exp((r - rf) * dt) b = Exp(-r * dt) p = (a - d) / (u - d) For i = 0 To N For j = 0 To i St(i, j) = S * u ^ j * d ^ (i - j) Next j Next i For j = 0 To N If (Call_Put = "Call") Then optlet_price(N, j) = Application.WorksheetFunction.Max(St(N, j) - X, 0) Else optlet_price(N, j) = Application.WorksheetFunction.Max(X - St(N, j), 0) End If Next j For i = N - 1 To 0 Step -1 For j = 0 To i optlet_price(i, j) = (p * optlet_price(i + 1, j + 1) + (1 - p) * optlet_price(i + 1, j)) * b Next j Next i Binomial_European = optlet_price(0, 0) End Function

16 Currency Option Pricing Binomial American Option Pricing VBA Code Function Binomial_American(S, X, Sday, Mday, vol, r, rf, Call_Put, N) Dim St(0 To 200, 0 To 200) As Double Dim optlet_price(0 To 200, 0 To 200) As Double tau = (Mday - Sday) / 365: dt = tau / N u = Exp(vol * Sqr(dt)): d = 1 / u a = Exp((r - rf) * dt): b = Exp(-r * dt) p = (a - d) / (u - d) For i = 0 To N For j = 0 To i St(i, j) = S * u ^ j * d ^ (i - j) Next j Next i For j = 0 To N If (Call_Put = "Call") Then optlet_price(N, j) = Application.WorksheetFunction.Max(St(N, j) - X, 0) Else: optlet_price(N, j) = Application.WorksheetFunction.Max(X - St(N, j), 0) End If Next j For i = N - 1 To 0 Step -1 For j = 0 To i optlet_price(i, j) = (p * optlet_price(i + 1, j + 1) + (1 - p) * optlet_price(i + 1, j)) * b If (Call_Put = "Call") Then optlet_price(i, j) = Application.WorksheetFunction.Max(St(i, j) - X, optlet_price(i, j)) Else: optlet_price(i, j) = Application.WorksheetFunction.Max(X - St(i, j), optlet_price(i, j)) End If Next j Next i Binomial_American = optlet_price(0, 0) End Function

17 Currency Option Pricing European Option Greeks VBA Code I Function Delta_Call(S, X, Sday, Mday, vol, r, rf) As Double Dim T As Double Dim d1 As Double T = (Mday - Sday) / 365 d1 = (Log(S / X) + (r - rf + vol ^ 2 / 2) * T) / (vol * T ^ 0.5) Delta_Call = Exp(-rf * T) * Application.NormSDist(d1) End Function Function Delta_Put(S, X, Sday, Mday, vol, r, rf) As Double Dim T As Double Dim d1 As Double T = (Mday - Sday) / 365 d1 = (Log(S / X) + (r - rf + vol ^ 2 / 2) * T) / (vol * T ^ 0.5) Delta_Put = Exp(-rf * T) * (Application.NormSDist(d1) - 1) End Function Function Gamma(S, X, Sday, Mday, vol, r, rf) Dim T As Double: Dim d1 As Double: Dim N1 As Double T = (Mday - Sday) / 365 d1 = (Log(S / X) + (r - rf + vol ^ 2 / 2) * T) / (vol * T ^ 0.5) N1 = (1 / (2 * Application.Pi()) ^ 0.5) * Exp((-d1 ^ 2) / 2) Gamma = (N1 * Exp(-rf * T)) / (S * vol * T ^ 0.5) End Function

18 Currency Option Pricing European Option Greeks VBA Code II Function Vega(S, X, Sday, Mday, vol, r, rf) Dim T As Double: Dim d1 As Double: Dim N1 As Double T = (Mday - Sday) / 365 d1 = (Log(S / X) + (r - rf + vol ^ 2 / 2) * T) / (vol * T ^ 0.5) N1 = (1 / (2 * Application.Pi()) ^ 0.5) * Exp((-d1 ^ 2) / 2) Vega = S * (T ^ 0.5) * N1 * Exp(-rf * T) End Function Function Theta_Call(S, X, Sday, Mday, vol, r, rf) Dim T As Double: Dim d1 As Double: Dim N1 As Double: Dim d2 As Double T = (Mday - Sday) / 365 d1 = (Log(S / X) + (r - rf + vol ^ 2 / 2) * T) / (vol * T ^ 0.5): d2 = d1 - vol * T ^ 0.5 N1 = (1 / (2 * Application.Pi()) ^ 0.5) * Exp((-d1 ^ 2) / 2) Theta_Call = -(S * N1 * vol * Exp(-rf * T)) / (2 * T ^ 0.5) + rf * S * Application.NormSDist(d1) * Exp(-rf * T) - r * X * Exp(-r * T) * Application.NormSDist(d2) End Function Function Theta_Put(S, X, Sday, Mday, vol, r, rf) Dim T As Double: Dim d1 As Double: Dim d2 As Double: Dim N1 As Double T = (Mday - Sday) / 365 d1 = (Log(S / X) + (r - rf + vol ^ 2 / 2) * T) / (vol * T ^ 0.5): d2 = d1 - vol * T ^ 0.5 N1 = (1 / (2 * Application.Pi()) ^ 0.5) * Exp((-d1 ^ 2) / 2) Theta_Put = -(S * N1 * vol * Exp(-rf * T)) / (2 * T ^ 0.5) - rf * S * Application.NormSDist(-d1) * Exp(-rf * T) + r * X * Exp(-r * T) * Application.NormSDist(-d2) End Function

19 Currency Option Pricing Currency Option Pricing Sample

20 Structured Currency Option - Sample

21 Epilogue Q&A ? Other issues in derivatives pricing with EXCEL ? More Information Call : Class Material & other files :