Question

a) Explain the difference between Value at Risk at q% level and expected shortfall at q% level?

b) Does Gamma increase or decrease on at the money options as they approach expiration?

Answer 1

a)Value at risk(VaR) is defind as the loss level that will not exceeded with a certain confidence level during a certain period of time.For instance,one might say-'for a given month,the VaR is 1 million at a 95% level of confidence',which can also be translated to 'under normal conditions in 95% of the months(e.g. 19 out of 20 months) we expect to loose no more than $1 million.

Expected Shortfall is also known as conditional VaR or expected tail loss.It is the expected loss given that the returns are already below the pre specified worst case scenarion(i.e. below the 5th percentile).Therefore,it represents the mean loss among the losses falling below a certain thresold(5%,1 % etc)

b)The option's gamma is a measure of the rate of change of its delta.The gamma of an option is expressed as a percentage and reflects the change in the delta in response to a one point movement of the underlying stock price.

Like the delta,the gamma is constantly changing,even with tiny movements of the the underlying stock price.

As the time to expiration draws nearer,the gamma of at the money options increases while the gamma of in the money and out of money options decreases.