Question

Use the Black-Scholes Option Pricing Model for the following problem. Given: S0 = $0.70/€; K = $0.70/€; T = 70 days; rd = 0.06, rf=0.03 annually;  = 0.205. What is the value of the put option?

Answer 1

The Black Scholes formula:

Call option = SP e-dt N(d1) - ST e-rt N(d2)

Put Option = ST e-rt N(-d2) - SP e-dt N(-d1)

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

d2 = ( ln(SP/ST) + (r - d - (σ2/2)) t ) / σ √t = d1 - σ √t

Where:

C is the value of the call option,

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).

Put Option = 0.7* e-0.03*70/365 N(-d2) - 0.7* e-0.06*70/365 N(-d1)

d1 = ( ln(0.70/0.70) + (0.03 - 0.06 + (0.2052/2)) 70/365 ) / 0.205 √70/365

d2 = ( ln(0.70/0.70) + (0.03 - 0.06 - (0.2052/2)) 70/365 ) / 0.205 √70/365 = d1 - σ √t

Put Price= $0.03