Sleaze Co. stock is currently valued at $40 per share. The volatility of SleazeCo. equity is 30 percent per year and the continuously compound risk-free rate is 1 percent per year. 

What is the Black/Scholes value of a European put option written on SleazeCo stock that has an exercise price of $35 and expires in a half a year (T = .5)? 

Put value = _______________________.

 

Question

Black / scholes value of the put option

Vc = P[N(d₁)]-xe^-rft. N(d₂)

D₁= [ln (p/x) + (rf + ?²/2)t]/(√?t)

D₂= d₁-√?t

VP= Vc-p+xe^-rft

Where

P= current price

X=exercise price

?= volatility

T=time remaining to expiration (in years)

N=standard cumulative normal function

E=exponential function

Rf=risk free rate

Vc=value of call

Vp= value of put

Ln =natural logarithm

D₁ and d₂ =standardized normal variable

P=$40

X=$35

T =0.5 years

Rf=1%

?=30%

d_{1 =} ln($40/$35)+ [0.01+(0.3²/2)]*0.5÷√0.3*0.5

=0.2877+0.0275 ÷0.3873

D₁ =0.8138

D₂=0.8138-0.3873=0.43

Check from the standard normal probability table

N(d₁)=N(0.81) =0.7910

N(d₂)= N(0.43)=0.6664

Vc = [$40*(0.7910)]-$35e^-0.01*0.5 . (0.6664) 

=$8.4323

Vp =$8.4323-$40+$35e^-0.01*0.5

Value of the put =$3.2577