AIM: Identify and describe the characteristics and pay-off structure of the following exotic options: forward start, compound, and chooser
Questions:
412.1. The price of a vanilla (non-exotic) at-the-money European call option, today, with a one year maturity is $15.05; if we extend the maturity to two years, the price of the option is $22.58. Now consider a forward start at-the-money European call option, on the same underlying stock, that will start in one year (T1 = 1.0 year) and mature one year later, two years from today (T2 = T1 + 1.0 year = 2.0 years). The continuous dividend yield on the underlying stock is 5.0% per annum, and the riskfree rate is 3.0% per annum; both are expressed with continuous compounding. Which is nearest to today's price of the forward start option?
a. $13.89
b. $14.32
c. $14.61
d. $21.48
412.2. Consider the four main types of compound options:
I. call on a call,
II. call on a put,
III. put on a call,
IV. put on a put
With respect to the value of the compound option as a function of the underlying asset price, which of these compound option's value is (are) a DECREASING function of the underlying asset price?
a. None, the compound values are all (each) an increasing function of asset price
b. IV. only (put on a put)
c. II. and III. (call on a put; put on a call)
d. III. and IV. (put on a call; put on a put)
412.3. Consider a chooser option where the underlying is Microsoft's stock (ticker: MSFT). The options underlying the chooser are both European and have the same strike price (i.e., simple chooser) of $35.00. The choose date is six months (T1 = 0.5 years) and the maturity of the options is one year (T2 = T1 + six months = 1.0 year). The riskfree rate is 3.0% per annum with continuous compounding. A long position in this chooser option is most similar to which of the following trading strategies, and how does the initial cost compare to the similar strategy?
a. Long straddle but chooser is cheaper
b. Short straddle but chooser is more expensive
c. Long calendar spread with similar cost
d. Long Butterfly spread but chooser cheaper
Answers here:
Questions:
412.1. The price of a vanilla (non-exotic) at-the-money European call option, today, with a one year maturity is $15.05; if we extend the maturity to two years, the price of the option is $22.58. Now consider a forward start at-the-money European call option, on the same underlying stock, that will start in one year (T1 = 1.0 year) and mature one year later, two years from today (T2 = T1 + 1.0 year = 2.0 years). The continuous dividend yield on the underlying stock is 5.0% per annum, and the riskfree rate is 3.0% per annum; both are expressed with continuous compounding. Which is nearest to today's price of the forward start option?
a. $13.89
b. $14.32
c. $14.61
d. $21.48
412.2. Consider the four main types of compound options:
I. call on a call,
II. call on a put,
III. put on a call,
IV. put on a put
With respect to the value of the compound option as a function of the underlying asset price, which of these compound option's value is (are) a DECREASING function of the underlying asset price?
a. None, the compound values are all (each) an increasing function of asset price
b. IV. only (put on a put)
c. II. and III. (call on a put; put on a call)
d. III. and IV. (put on a call; put on a put)
412.3. Consider a chooser option where the underlying is Microsoft's stock (ticker: MSFT). The options underlying the chooser are both European and have the same strike price (i.e., simple chooser) of $35.00. The choose date is six months (T1 = 0.5 years) and the maturity of the options is one year (T2 = T1 + six months = 1.0 year). The riskfree rate is 3.0% per annum with continuous compounding. A long position in this chooser option is most similar to which of the following trading strategies, and how does the initial cost compare to the similar strategy?
a. Long straddle but chooser is cheaper
b. Short straddle but chooser is more expensive
c. Long calendar spread with similar cost
d. Long Butterfly spread but chooser cheaper
Answers here:
