Tony owns a 3-month European put option on a HexGem Technologies (HGT) share with a strike price of $250. The current price for a HGT share is $244. Tony knows that in any month, the share price will either go up by 5% or down by 3% (so after 1 month, the share price is either $256.20 or $236.68).

The risk-free continuously compounding rate of interest is 6% p.a.

a) Construct the 3-step step binomial tree showing the possible share prices over the next 4 months. Using this tree, also write down the intrinsic value of Tonys option for each possible share price in 3 months time.

2. b) Calculate the risk-neutral probability for an upward movement in the share price

3. c) Using the results from part a) or otherwise, calculate the value of Tonys put option.

d) Natasha currently owns a 3-month European call option on a HGT share with a strike price of $250. Without using the result from part c), calculate the value of Natashas call option.

e) Using the results from parts c) and d), verify the put-call parity.