The paper "Derivative Securities in Finance" is a perfect example of a finance and accounting assignment. The option prices are consistent with assumptions underlying the Black Scholes model. The implied volatility depends on the maturity and value of the option. If maturity is for a short duration, volatility is higher than for options that have a longer maturity period. If the value of the option is high, implied volatility is high. On the other hand, if it is low, the implied volatility is low. Difference between implied and historical volatility Implied volatility is estimated potential movement of an option’ s price.
It focuses on future stock changes. On the other hand, historical volatility is the standard deviation of annual stock movements. It is the level at which stock price changed on a daily basis in a previous year. It is based on historical data changes. Implied volatility is also said to be higher than historical volatility. This can be observed from the volatility figures in the above table (Historical vs. Implied Volatility, 2011). Question 2 Portfolio insurance strategy The two portfolio strategies explained below are naï ve hedge and risk hedge. S& P 500 futures multiplier= $250 P: Current portfolio value= $55,000,000 Beta= 1.5 Dividend yield of the portfolio= 2.4% simple compounding S& P dividend yield= 1.8% p. a.
simple compounding Risk free interest rate= 4.8% p. a. continuous compounding A: current value of futures contract on index= 1327*250= 331,750 F: Current price of S& P 500 index= 1327 Naï ve hedge (N): Hedging $55m portfolio with S& P 500 futures will mean that the investor will sell 55,000,000/ 331750= 166 contracts. If N is less than zero the investor should sell and if it is greater than zero, he should buy. N= (desired beta-portfolio beta) (Current portfolio value/ Current value of futures contract on index) N= (0-1.5) * (55,000,000)/ 331,750=-249 contracts (sell). Therefore, the investor should sell 249 contracts. Position necessary to reduce beta to 0.75: (0.75-1.5) * (55,000,000)/ 331,750= -124 contracts (sell) Position necessary to increase beta to. 2.0: (2.0-1.5) * (55,000,000)/ 331,750= 83 contracts (buy) Risk hedge = (Dollar value of the portfolio/ Dollar value of the S& P futures contract) * beta= [$55,000,000/ (1327*250)] * 1.5= 248.68 = 249 contracts.
Given beta, the investor should sell 249 contracts.
ReferenceHistorical vs. Implied Volatility. (2011). Retrieved May 24. 2012, from http://community.tradeking.com/members/optionsguy/blogs/83304-historical-vs-implied-volatility-what%E2%80%99s-the-difference