# Black-Scholes

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```					Optiepremie securities opties volgens Black and Scholes model

Securities price                  40   S
Strike price                      45   K
Risk-free interest rate       5.00%    r
Volatility                      20%    σ (jaarbasis)
Days                              90   n
Duration                      0.2466   t          t = n/365
PV strike                     44.46    PV(K)      PV(K) = K / (1 + r)^t

Call premium                   0.31               C = S x N(d1) + PV(K) x N(d2)
Put premium                    4.77               P = - S x (1-N(d1)) + PV(K) x ( 1- N(d2))

N = cumulative probability according to standard normal distribution
-   1.015   d1 = ln(S/PV(K))/σ√t + σ√t/2   0.155008    15,500.81
-   1.115   d2 = ln(S/PV(K))/σ√t - σ√t/2   0.132532   589,262.99

30,769.36
Optiepremie FX opties volgens Black and Scholes model

FX forward rate               1.3000   S
Strike price                  1.3500   K
Volatility                      10%    σ (jaarbasis)
Days                              90   n
Duration                      0.2466   t          t = n/365

Call premium                 0.0085               C = S x N(d1) + K x N(d2)
Put premium                  0.0585               P = - S x (1-N(d1)) + K x ( 1- N(d2))

N = cumulative probability according to standard normal distribution
-   0.735 d1 d1 = ln(S/K)/σ√t + σ√t/2   N(d1)   0.23110823 0.3004407
-   0.785 d2 d2 = ln(S/K)/σ√t - σ√t/2   N(d2)   0.21626831 0.29196221

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