Question

Black-Scholes 2.45-Y 100% Q- Search in Sheet Home Layout Tables Charts SmartArt Formulas Data Review Edit Font Number Format Cells Themes Alignment abc Fill Calibri (Body) 12 A A Wrap Text Number Normal XD Aa Clear B 1 U Les % Merge 4.0 .00 .00 >.0 Paste Bad Conditional Formatting Insert Delete Format Aa Themes C8 fx =B8*EXP(E4F4) E А B C F H 1 J K L M N O Р Q R S d1 OTM بریم به هه لا S 40.00 40.00 40.00 к 35.00 40.00 45.00 0 30.00% 30.00% 30.00% r 0.36% 0.36% 0.36% T 0.595 0.595 0.595 6 0.00% 0.00% 0.00% 0.702 0.125 -0.384 d2 0.471 -0.106 -0.616 с 6.56 3.72 1.93 P 1.49 3.64 6.84 ITM ATM OTM Ce^irt) 6.57 3.73 1.94 Pert) 1.49 3.64 6.85 ATM ITM S 40.00 F_O,T 40.09 7 8 9 10 11 12 13 r S 40.00 40.00 к 38.00 43.00 30.00% 30.00% 0.36% 0.36% T 0.595 0.595 6 0.00% 0.00% d1 0.347 -0.188 d2 0.115 -0.419 С 4.72 2.54 P 2.64 5.44 Ce^(rt) 4.73 2.54 Pe^(rt) 2.65 5.46

Black-Scholes

1. C8: Provide a formula for the forward price based on the stock price S, the risk-free rate r and the time to expiration T.

2. Columns N, O: Provide formulas for the future value (at expiration) value of the option premiums using the BlackScholes option prices C(K,T) and P(K,T), the risk free rate r and the time to expiration T.

Answer 1

Answer

1) Formula for Forward price:

F = S(1+r)^T

^Where,

^{F = Forward Price}

^{S = Spot/stock price}

^{r = Risk free rate}

^{T = Time to expiration}

^OR

^{IF continuous compound rate of interest is used:}

F = S*e^rt

^Where,

^{F = Forward Price}

^{S = Spot/stock price}

^{r = Risk free rate}

^{T = Time to expiration}

^{e = Exponetial constant having standard value of 2.7183}

²⁾

Call option price:

C(K,T) = S​*N(d1​)−Ke^−rt *N(d2​)

Where,

d1 = [ln St / K ​​+(r+σ²v / 2​​) t]/ σs​ √t

d2 = d1 - σs​ √t

​where:

C=Call option price

S=Current stock (or other underlying) price

K=Strike price

r=Risk-free interest rate

t=Time to maturity

N=A normal distribution​

Put Option Price:

P(K,T) = Ke^−rt *N(−d2​) − S​*N(−d1​)