Suzanne Evans
Well-Known Member
Questions:
201.1. Portfolio manager Sam has a long position in an at-the-money (ATM) call option contract, with a standard size of 100 options, in which the strike price is the same as the current stock price of $100.00. The option is European with a one year term. The volatility of the stock is 30.0% per annum. The percentage (per option) delta is 0.60 and the gamma is 0.02. Sam assumes 250 trading days in the year, that stock returns are i.i.d. normal, and he ignores positive drift (mu) over the short-run such that he computes a relative VaR. If Sam includes the gamma term (aka, quadratic VaR), what is the 10-day 99.0% confident value at risk (VaR) of the option contract?
a. $600.00
b. $643.36
c. $838.80
d. $1,398.00
201.2. Jane has a short position in 100 put option contracts (10,000 options) where, according to Black-Scholes Merton, N(d1) = 0.650 and the per option (percentage) gamma is 0.0150. The one-day 95.0% value at risk (VaR) on a single share of the underlying non-dividend-paying stock is $4.00. Assuming i.i.d. returns, what is the 10-day 95% VaR of the short put option contract?
a. $25,880
b. $44,300
c. $56,272
d. $91,667
201.3. Bond has a long position in a bond with a face value of $1,000.00. He assumes the daily yield volatility is 1.0% with normally distributed daily yields. The bond's modified duration is 9.70 years and its convexity (C) is 100.0 years^2. The current price of the bond is $612.00. What is the 95% daily (quadratic) value-at-risk?
a. $89.37
b. $97.65
c. $152.30
d. $206.59
Answers:
201.1. Portfolio manager Sam has a long position in an at-the-money (ATM) call option contract, with a standard size of 100 options, in which the strike price is the same as the current stock price of $100.00. The option is European with a one year term. The volatility of the stock is 30.0% per annum. The percentage (per option) delta is 0.60 and the gamma is 0.02. Sam assumes 250 trading days in the year, that stock returns are i.i.d. normal, and he ignores positive drift (mu) over the short-run such that he computes a relative VaR. If Sam includes the gamma term (aka, quadratic VaR), what is the 10-day 99.0% confident value at risk (VaR) of the option contract?
a. $600.00
b. $643.36
c. $838.80
d. $1,398.00
201.2. Jane has a short position in 100 put option contracts (10,000 options) where, according to Black-Scholes Merton, N(d1) = 0.650 and the per option (percentage) gamma is 0.0150. The one-day 95.0% value at risk (VaR) on a single share of the underlying non-dividend-paying stock is $4.00. Assuming i.i.d. returns, what is the 10-day 95% VaR of the short put option contract?
a. $25,880
b. $44,300
c. $56,272
d. $91,667
201.3. Bond has a long position in a bond with a face value of $1,000.00. He assumes the daily yield volatility is 1.0% with normally distributed daily yields. The bond's modified duration is 9.70 years and its convexity (C) is 100.0 years^2. The current price of the bond is $612.00. What is the 95% daily (quadratic) value-at-risk?
a. $89.37
b. $97.65
c. $152.30
d. $206.59
Answers:
