Exam 16: Beyond Black-Scholes

An option-trading firm is using the Black-Scholes (1973)model to price their options using the same level of volatility for all strikes.The market anticipation is that sharp negative gapping behavior is likely given that sudden recessionary information is being released in spurts.By using the Black-Scholes model with a constant volatility the firm is

In comparing the ARCH $( q )$ model with GARCH $( p , q )$ for $p \geq 1$ ,which of the following statements is most likely to be valid?

For the same problem in the preceding two questions,find the state price at the middle node after two periods,given that the 117.3008--strike call is priced at $4 and the 85.2509--strike put is priced at $4,both options of two-months maturity.Assume that the middle node after two periods has the same stock price as the initial stock price.

An option-trading firm is using the Black-Scholes (1973)model (with the same constant volatility for all strikes)to price index options.Market sentiment is that the stock return volatility is stochastic and changes in volatility are negatively correlated with stock returns.By using the Black-Scholes model with a constant volatility the firm is

A Wall Street trading firm is using a jump-diffusion model to price their index options.They determine that the arrival rate of jumps in the market is 4 times a year,and that the jumps have a mean size of $- 2 \%$ and standard deviation of 10%.If the implied volatility of the stock index is 40%,what is the diffusion parameter ( $\sigma$ )that they should use in their model?

If the volatility of a stock is not constant and changes randomly over time,it generates the implied volatility "smile" or "skew".Which of the following statements about the smile is most valid?

The asymmetric GARCH model was developed to mimic the following feature of other models that is not captured in the standard GARCH formulation: