Question Three Suppose that stock X pays no dividends, has volatility V3%, and its price today is SP3 (a) Calculate the prices of both European call options and European put options written on stock X if the strike price is SS3, the time to expiry is M3 months, and the spot interest rate is R3 (b) Assuming the same conditions as in part (a) recalculate the European call and European put option prices if the investor's portfolio is hedged every trading fortnight at a cost of 13% of the traded securities 110 marks Question Four Suppose that the price of stock X today is SP4. You are offered an American option on one share of stock X with a strike price SS4 which expires in M4 months' time. It is known that the volatility of stock X is V4%, and the spot interest rate is R4%. Calculate the up and down multipliers and d for a 5-step binomial tree of stock prices for stock X if the branching probability is p=1/2. (b) Construct the binomial tree of stock prices for stock X. Use the 5-step binomial method to estimate the price today of an American option written on stock X if: (i) the option is a call (ii) the option is a put 115 marks Question Three Suppose that stock X pays no dividends, has volatility V3%, and its price today is SP3 (a) Calculate the prices of both European call options and European put options written on stock X if the strike price is $S3, the time to expiry is M3 months, and the spot interest rate is R3% (b) Assuming the same conditions as in part (a) recalculate the European call and European put option prices if the investor's portfolio is hedged every trading fortnight at a cost of H3% of the traded securities. [10 marks Question Four Suppose that the price of stock X today is $P4. You are offered an American option on one share of stock X with a strike price $S4 which expires in M4 months' time. It is known that the volatility of stock X is V4%, and the spot interest rate is R4%. Calculate the up and down multipliers u and d for a 5-step binomial tree of stock prices for stock X if the branching probability is p=1/2. (b) Construct the binomial tree of stock prices for stock X. (c) Use the 5-step binomial method to estimate the price today of an American option written on stock X if: (i) the option is a call (ii) the option is a put [15 marks Question Three Suppose that stock X pays no dividends, has volatility V3%, and its price today is SP3 (a) Calculate the prices of both European call options and European put options written on stock X if the strike price is SS3, the time to expiry is M3 months, and the spot interest rate is R3 (b) Assuming the same conditions as in part (a) recalculate the European call and European put option prices if the investor's portfolio is hedged every trading fortnight at a cost of 13% of the traded securities 110 marks Question Four Suppose that the price of stock X today is SP4. You are offered an American option on one share of stock X with a strike price SS4 which expires in M4 months' time. It is known that the volatility of stock X is V4%, and the spot interest rate is R4%. Calculate the up and down multipliers and d for a 5-step binomial tree of stock prices for stock X if the branching probability is p=1/2. (b) Construct the binomial tree of stock prices for stock X. Use the 5-step binomial method to estimate the price today of an American option written on stock X if: (i) the option is a call (ii) the option is a put 115 marks Question Three Suppose that stock X pays no dividends, has volatility V3%, and its price today is SP3 (a) Calculate the prices of both European call options and European put options written on stock X if the strike price is $S3, the time to expiry is M3 months, and the spot interest rate is R3% (b) Assuming the same conditions as in part (a) recalculate the European call and European put option prices if the investor's portfolio is hedged every trading fortnight at a cost of H3% of the traded securities. [10 marks Question Four Suppose that the price of stock X today is $P4. You are offered an American option on one share of stock X with a strike price $S4 which expires in M4 months' time. It is known that the volatility of stock X is V4%, and the spot interest rate is R4%. Calculate the up and down multipliers u and d for a 5-step binomial tree of stock prices for stock X if the branching probability is p=1/2. (b) Construct the binomial tree of stock prices for stock X. (c) Use the 5-step binomial method to estimate the price today of an American option written on stock X if: (i) the option is a call (ii) the option is a put [15 marks
