Suppose the cost of carry of a commodity is b. Show that the governing differential equation for the price of the option on the commodity under the Black– Scholes formulation is given by 

where V (S,t) is the price of the option, σ and r are the constant volatility and riskless interest rate, respectively. Find the put-call parity relation for the price functions of the European put and call options on the commodity.

Transcribed Image Text:

Ꮩ at + -52 [ 2 Ꭷ2v Ꭷ Ꮪ2 +bs ᎧᏙ Ꭷ Ꮪ - rV = 0,