A European put option on XYZ stock has the following specifications: Strike price = $45, current stock price = $46, time to expiration = 3 months, annual continuously compounded interest rate = 0.08, dividend yield = 0.02, prepaid forward price volatility=0.35. Calculate the elasticity of such a put.
Where
C(St , K, σ, r, T − t, δ) = Ste −δ(T −t)N(d1) − Ke−r(T −t)N(d2) where
d1 = [ln (St/K) + (r − δ + 0.5σ 2 )(T − t)]/ [σ √ (T − t)] and
d2 = [ln (St/K) + (r − δ − 0.5σ 2 )(T − t)]/ [σ √ (T − t)] = d1 − σ √ (T − t)
• St is the stock price at time t.
• K is the strike price of the option.
• σ is the annual standard deviation of the rate of return on the stock or the prepaid forward price volatility.
• r is the annual continuously compounded risk-free interest rate.
• T is the time to expiration.
• δ is the annual continuously compounded dividend yield.