Suzanne Evans
Well-Known Member
Questions:
202.1. Analyst Brian employs a recombining binomial tree to estimate the absolute value at risk of an asset ("absolute" signifies potential loss relative to the initial value). The initial value of the asset is $100.00. The horizon is 2.0 years and the tree has 8 steps; each time step in the tree is therefore three months (0.25 years). The real-world probability (p*) of an up movement is 44.0%. The up step size (u) = 1.20 and the down step size (d) = 1/u = 0.833.; both are per (0.25) step. Which is nearest to the two-year 99.0% absolute value at risk (VaR)?
a. $17.25
b. $33.18
c. $47.00
d. $66.51
202.2. Bob tries to value a three month European put option with a one-step binomial tree (one step = 0.25 years). The price of the non-dividend-paying stock is $100.00 and the put option is at-the-money (ATM) with a strike price of $100.00. The asset volatility is 36.0% per annum with continuous compounding. The riskless rate is 4.0%. Bob decides that volatility will inform the size of the up (u) and down (d) steps according to a Cox, Ross Rubinstein (CRR) model; i.e., if the number of steps were increases the asset price would tend toward a lognormal distribution.
a. $2.89
b. $8.43
c. $15.05
d. $20.76
202.3. Risk Manager Mark is pricing a six-month American put option on a non-dividend-paying stock when the stock price is $105.00. The put option is out of the money (OTM) as the strike price is $100.00. Mark assumes a two-step tree such that each step is three months. He assume a 6.0% riskless rate with continuous compounding. Instead of "matching volatility with up (u) and down (d) size movements," Mark simply assumes the size of the up movement is +20% and the size of the down movement is -20%; i.e., u = 1.20 and d = 0.80. What is nearest to the estimate of the price of the American put option? (variation on GARP 2012 Sample Questions 7 and 8)
a. $5.34
b. $6.80
c. $7.29
d. $8.51
Answers:
202.1. Analyst Brian employs a recombining binomial tree to estimate the absolute value at risk of an asset ("absolute" signifies potential loss relative to the initial value). The initial value of the asset is $100.00. The horizon is 2.0 years and the tree has 8 steps; each time step in the tree is therefore three months (0.25 years). The real-world probability (p*) of an up movement is 44.0%. The up step size (u) = 1.20 and the down step size (d) = 1/u = 0.833.; both are per (0.25) step. Which is nearest to the two-year 99.0% absolute value at risk (VaR)?
a. $17.25
b. $33.18
c. $47.00
d. $66.51
202.2. Bob tries to value a three month European put option with a one-step binomial tree (one step = 0.25 years). The price of the non-dividend-paying stock is $100.00 and the put option is at-the-money (ATM) with a strike price of $100.00. The asset volatility is 36.0% per annum with continuous compounding. The riskless rate is 4.0%. Bob decides that volatility will inform the size of the up (u) and down (d) steps according to a Cox, Ross Rubinstein (CRR) model; i.e., if the number of steps were increases the asset price would tend toward a lognormal distribution.
a. $2.89
b. $8.43
c. $15.05
d. $20.76
202.3. Risk Manager Mark is pricing a six-month American put option on a non-dividend-paying stock when the stock price is $105.00. The put option is out of the money (OTM) as the strike price is $100.00. Mark assumes a two-step tree such that each step is three months. He assume a 6.0% riskless rate with continuous compounding. Instead of "matching volatility with up (u) and down (d) size movements," Mark simply assumes the size of the up movement is +20% and the size of the down movement is -20%; i.e., u = 1.20 and d = 0.80. What is nearest to the estimate of the price of the American put option? (variation on GARP 2012 Sample Questions 7 and 8)
a. $5.34
b. $6.80
c. $7.29
d. $8.51
Answers:
