5. A) Find the price of an American call on a stock that matures in two months...
Question:
i)daily
ii)weekly
iii)monthly
(no dividends, 1 month = 20 days = 4 weeks). The exercise price is 300, the spot price of the stock is 310, the risk-free rate is 8% per annum and stock volatility is 30% per annum.
Using the same method you used in the American call, find the price of a European call whose price changes
i)daily
ii)weekly
iii)monthly
with a strike price of 300, a spot price of 310, a risk-free rate of 8% per annum and stock volatility of 30% per annum.
Select one of the two calls, price it according to the BlackScholes formula, calculate its (delta) and explain the 's use and intuition. For the other call, calculate its based on the first monthly price change. Compare and comment on your results, with extra focus on method applicability, accuracy and discrepancies. For visual representations, you can ignore the daily cases. [10 points]
5.B)A trader holds two calls and one put on the same share, all of which expiring in three months. The exercise price of both calls is $70 and the exercise of the put is $80. Each option is sold as a 100-share contract.
(i)Find the payoff at the expiration date if the stock sells for $65 and if it sells for 90$. Draw the payoff diagram (profile) for your option position. (3 points)
(ii)Using the above example as a base case (strike prices, long-short, type of assets etc), turn the position into
(a) a short straddle and a long strangle (show both)
(b) a butterfly with calls
(c) a bear put spread
(d) a collar
(e) butterfly with calls
(f) iron condor by making any changes you see fit.
You can add or remove any assets you need but try to make as few changes as possible. Explain in detail the changes you make and the reasoning behind them. Construct the payoff profile for each position and explain its usefulness and aims. (7 points) [10 points]
Expert Answer:
5A Pricing American and European Calls To price the American and European calls we will use the BlackScholes model The BlackScholes formula for the price of a call option is C S Nd1 X erT Nd2 Where C ... View the full answer
