SleazeCo. 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 = _______________________.

 

Put Value = 1.220

Calculation

P = ST e^-rt N(-d₂) - SP e^-dt N(-d₁)

d₁ = ( ln(SP/ST) + (r - d + (σ²/2)) t ) / σ √t

d₂ = d₁ - σ √t

Where:

P is the value of the put option,

N (.) is the cumulative standard normal distribution function,

SP is the current stock price (spot price),

ST is the strike price (exercise price),

e is the exponential constant (2.7182818),

ln is the natural logarithm,

r is the current risk-free interest rate (as a decimal),

t is the time to expiration in years,

σ is the annualized volatility of the stock (as a decimal),

d is the dividend yield (as a decimal).

d₁ = ( ln(SP/ST) + (r - d + (σ²/2)) t ) / σ √t

d1 = (ln(40/35) + (0.01 - 0 + (0.3²/2)) 0.5) / 0.3 √0.5

d1 = 0.759

d₂ = d₁ - σ √t

d2 = 0.759 - 0.3 √0.5

d2 = 0.547

P = ST e^-rt N(-d₂) - SP e^-dt N(-d₁)

P = 35 e^-(0.01*0.5) N(-0.547) - 40 e^-(0*0.5) N(-0.759)

P = 1.220