Explain with proof that c >= max(S - X, 0), where c is the value of the European call option, S is the price of the underlying asset and X is the strike of the option.
The following data pertaining to the ST Stock Index Options:
3000/3100 Put (vertical) Spread premium:
3100/3200 Put (vertical) Spread premium:
(i) Determine the premium of the 3000/3100/3200 Long Butterfly Spread.
(ii) Upon expiration, the ST index settles at 3050, what is the profit/loss of this Long Butterfly strategy?
(a) The Nikkei 500 Stock Index is now 10300 points. If the risk-free rate is 0.5%, and the dividend yield is 2%,
(i) What is the Nikkei 500 Index Futures expiring in 50 days?
(ii) If this Index Futures settled at 10200, what is the profit/loss if a trader shorted at the price in part (i) for 50 contracts (Every index point worth JPY500).
(b) If the yield curve is expected to be flattening, what SPREAD trading strategy would you adopt with Eurodollar Interest Rate Futures?
(c) A portfolio manager wishes to hedge his $4.5 million stock portfolio with ST Index Futures. Given that the standard deviation of the returns of his portfolio is 0.2 and that of the ST Index Futures is 0.3, and the correlation between the two is 0.75.
(i) What is the Minimum Variance Hedge Ratio?
(ii) What is the effectiveness of the hedge?
(iii) How many ST Index Futures contracts are required to hedge if the ST Futures is at 3000 index points (Every index point worth $10).
(iv) To short or to long the ST Index Futures?
(d) How would you hedge the increasing volatility of the stock market with Stock Index Options?