Hi Can you kindly help on the below Acted notes - page 54 – q 14.2 [iii] i.e. part 3 A special option is available where the payoff after 5 days is: Max[S5*-K,0] where S5* is the arithmetic average share price recorded at the end of each of the 5 days and K is the strike price. Calculate the fair price of special option [strike price K=1.06So) on 10,000 pounds worth of shares in this company. I did not understand question and answer – could you kindly help? Best wishes Bobby
Here we are valuing an unusual derivative using the binomial model. This question illustrates that the binomial model can be used to value any derivative (not just standard call options and put options) - all we need to know is the payoff from the derivative. The question states the payoff is max(S5* - K,0), where K = 1.06 x S0 = 1.06 x 10,000 = 10,600 (where S0 - the current value of the shares - is given in the question). S5* is the arithmetic average share price at the end of each of the 5 days. So if we consider one particular path through the binomial tree leading to a particular final node and the share prices were A (day 1), B (day 2), C (day 3), D (day 4) and E (day 5), then the value of S5* would be 10,000 x (A+B+C+D+E)/5, ie we average out the 5 share prices on the way to the final node. The solution says that the only non-zero payoff (where S5* exceeds 10,600) occurs when the share price rises 5 days in a row. You can check this for yourself - Excel might be an efficient way of doing this. Then the value of the derivative is calculated in the standard way using the risk-neutral approach. It is the discounted value of the expected payoff, where the probabilities are the q (risk-neutral) probabilities. So we take sum (over all nodes) of payoff at that node x risk-neutral prob of getting to that node x discount factor. There's only one term in the sum here, as there is only one non-zero payoff. Does that help?
