QUESTION A European call option on a stock has an exercise date one year away and a strike of $6. The underlying stock has a current price of $5.50. The option is priced at 60p. The stock price volatility has been estimated from other option prices as 20%. The estimated risk free rate of interest from part (i) is 14.55%. (iii) A new derivative security has just been written on the underlying stock. This will pay a random amount D in one year's time, where D = S1^2. Calculate the fair price for this new derivative security, quoting any further results used. QUERY Can I check if using the formulae for u and d on page 45 of the tables to determine S0u and S0d and then determining the expected present value of the derivative by discounting the expectation under risk-neutral probabilities would also be a fair approximation here? The solutions provided use the expectation under the lognormal model to derive the answer.
The question also says "assuming the Black-Scholes model applies", admittedly that's in part (ii). This means that the binomial model assumption you've outlined would not be appropriate here.
