Calculation of option value的公式是什么？

Value a Call Option with BSOP

Formula provided

Value of a call option at time 0

Value a Put Option with BSOP

In the exam, you are provided with the following formula to help value a put option

Formula provided

P=C-P_a +P_ee^-rt

C=value of a call option　　　　P=value of a put option

As you can see, a call option has to be valued before valuing a put.

Example for Option Valuation

Ø The underlying asset price now is 68.5 with a volatility of 0.38.The continuously compounded risk-free rate is 4%.Consider the value of a 110-day European call and put with the exercise price of 65.

Ø Correct Answer:

•       We should first calculate d₁ and d₂: (110 days equal to 0.3014 year)

d₁=[ln(68.5/65)+(0.04+0.38²×0.5)×0.3014]/(0.38×)=0.41

d₂=0.41-0.38×=0.20

•        Then look up N(d₁) and N(d₂) in the cumulative normal probability table:

N(0.41)=0.6591　　　　

N (0.20)=0.5793

•       Then we can get the value of the call:

C₀=68.5×0.6591-65e^{-0.04×0.3014}×0.5793=7.95

•       We can use put-call parity or the BSM formula to get the put price:

P₀=C₀+PV(X)-S₀=7.95+65e^{-0.04×0.3014}-68.5=3.67

Or,P₀=65e^{-0.04×0.3014}×（1- 0.5793）-68.5 ×（1-0.6591）=3.67