Reference no: EM132474829

As a base case, do your analysis using mid prices = (bid+ask)/2. Or you can enrich your analysis by performing calculations on bid and on ask prices separately. The difference between the results using the bid from those using the ask prices should be a reflection of the effect of ‘transaction costs,' and hence you can discuss these effects.

Step 1 Coursework Requirements

The requirements are:

Question a. Investigate (calculating and checking) whether the put-call parity holds for the actual market prices of both the European and the American options. Interpret the results (more emphasis and marks will be given to interpretation).

Question b. Calculate the difference between the actual market prices of the American and European options that have the same exercise price and maturity. Interpret the results (more emphasis and marks will be given to interpretation).

Question c. Calculate the theoretical Black and Scholes prices of all the selected European and American options and compare these theoretical values with the actual market prices of the options. Interpret any differences (more emphasis and marks will be given to the interpretation).

STEP 2

Binomial Model Setup Features

1. Using the 'binomial model', build a binomial tree for the index level with three time steps, so that the overall time horizon is equal to the maturity of the options selected (i.e., divide the maturity into three equal intervals).
2. With regard to the binomial calculations choose the upward and downward size of price movement as a function of the volatility of the index level (i.e., function of sigma of the index). You can use the equations provided by Chance and Brooks for up (u) and down (d) parameter movements as functions of sigma, also provided in the lecture material. For estimates of sigma seeEstimating Volatility of the Index above. You will also need an estimate of the dividend yield on the index. For these see Estimating Annualised Dividend Yield above.

Step 2 Course Requirements

Binomial Pricing

Question 1: Using the VXO estimate of volatility evaluate the call and put options using the three-step binomial tree previously constructed for the index level (here you need to have your tree calculations automated so you can evaluate all options). Compare the binomial option prices with the actual option prices observed in the market and discuss the reasons why you do, or do not, observe any differences. (More emphasis and marks will be given to discussion.)

Black and Scholes versus Binomial

Question 2: Using the VXO estimate of volatility calculate the Black-Scholes prices of the put and call options. Compare these values with the actual market prices and with those obtained by the Binomial model. Discuss possible reasons for any differences (i.e., compare Black-Scholes versus Binomial, American versus European, puts versus calls, ATM versus OTM). (More emphasis and marks will be given to the discussion of each of these comparisons)

Implied volatility

Question 3: By trial and error, find the value of the volatility parameter at which the Black and Scholes price equals the observed actual market price for each option. The value of volatility at which the observed actual market price equals the Black and Scholes price is known as ‘implied volatility'. Create plots of the implied volatility of the options against their exercise price. Compare these values of implied volatility with each other. Also compare them with the value obtained from the VXO index. Discuss the reasons for any differences from each other and from the VXO value. (More emphasis and marks will be given to discussion.)