FRM Book 3 Chapter 15| Questions with Complete Solutions 100% Verified|
Latest Update Graded A+
What is the payoff from a portfolio consisting of a long position in both a floating lookback call
and a floating lookback put? A floating lookback call provides a payoff of ST - Smin and a
floating lookback put provides a payoff of Smax - ST. The payoff from the portfolio is therefore
the excess of the maximum asset price over the minimum asset price (ST - Smin + Smax - ST =
Smax - Smin)
Derive expressions for the payoffs from a: a. Long position in an average price call and short
posi-tion in an average price put,
b. A long position in an average strike call and short position in an average strike put, and
c. A long position in a plain vanilla European call and short position in a plain vanilla European
put.
d. All options have the same strike price and time to maturity. Use the results to derive a
relationship between the prices of the six options you have considered. (a) A long average
price call gives a payoff of max(Save - K, 0). A short average price put gives a pay-off of -max(K -
Save, 0). The payoff in (a) is therefore always Save - K whether Save > K or Save < K. Similarly,
the payoff in (b) is always ST - Save and the payoff in (c) is always ST - K. From this, it follows
that:
(c1 - p1) + (c2 - p2) = (c - p)
where c1 and p1 are the prices of the average price call and put, c2 and p2 are the prices of the
average strike call and put, and c and p are the prices of the plain vanilla call and put.
Explain why a gap call option is a regular call option plus a binary option when K2 > K1, using
the same notation as in the chapter Consider a gap option where the trigger price is K2 and
the strike price for determining payoffs is K1. The gap call option is a plain vanilla option with
strike price K2 plus a cash-or-nothing binary option that pays off K2 - K1 if the asset price is
above K2
Latest Update Graded A+
What is the payoff from a portfolio consisting of a long position in both a floating lookback call
and a floating lookback put? A floating lookback call provides a payoff of ST - Smin and a
floating lookback put provides a payoff of Smax - ST. The payoff from the portfolio is therefore
the excess of the maximum asset price over the minimum asset price (ST - Smin + Smax - ST =
Smax - Smin)
Derive expressions for the payoffs from a: a. Long position in an average price call and short
posi-tion in an average price put,
b. A long position in an average strike call and short position in an average strike put, and
c. A long position in a plain vanilla European call and short position in a plain vanilla European
put.
d. All options have the same strike price and time to maturity. Use the results to derive a
relationship between the prices of the six options you have considered. (a) A long average
price call gives a payoff of max(Save - K, 0). A short average price put gives a pay-off of -max(K -
Save, 0). The payoff in (a) is therefore always Save - K whether Save > K or Save < K. Similarly,
the payoff in (b) is always ST - Save and the payoff in (c) is always ST - K. From this, it follows
that:
(c1 - p1) + (c2 - p2) = (c - p)
where c1 and p1 are the prices of the average price call and put, c2 and p2 are the prices of the
average strike call and put, and c and p are the prices of the plain vanilla call and put.
Explain why a gap call option is a regular call option plus a binary option when K2 > K1, using
the same notation as in the chapter Consider a gap option where the trigger price is K2 and
the strike price for determining payoffs is K1. The gap call option is a plain vanilla option with
strike price K2 plus a cash-or-nothing binary option that pays off K2 - K1 if the asset price is
above K2
