An investment firm is developing a new Exotic Derivative Contract.
An investment firm is developing a new Exotic Derivative Contract.
This contract will pay off stock price at expiry squared, ST
2
, given stock price is less than the strike price, K.
That is defined by the following function:
Given that the underlying stock is assumed to follow Geometric Brownian Motion;
(A) Use Risk-Neutral Valuation to derive the fair price of the security at time t in terms of the stock price,
S, at time t. This will be referred to as G. (2 Marks)
(HINT: You will first need to derive the stochastic process that is followed by Yt = St
2
,
Your derivation in (a) should show that đť‘Śt also follows a GBM)
(B) Determine whether or not this value satisfies the Black-Scholes-Merton Partial Differential Equation;
(2 Marks)
(C) Explain, in words, what the result of part (B) means for this contract’s tradeability.
