Answer-first summary for fast verification
Answer: 0.24%
## Explanation This is a binomial interest rate option valuation problem. The option value at Time 0 can be calculated using risk-neutral valuation: **Step 1: Calculate option payoffs at Time 2** - After two up moves: Max(3.9706% - 3.1000%, 0) = 0.8706% - After up and down moves: Max(3.2542% - 3.1000%, 0) = 0.1542% - After two down moves: Max(0% - 3.1000%, 0) = 0% (assuming rate goes to 0%) **Step 2: Calculate option value at Time 1** - When up move occurs: Value = 0.4209% (given) - When down move occurs: Value = 0.0751% (given) **Step 3: Calculate option value at Time 0** Using risk-neutral valuation with 50% probability: Option value at Time 0 = [0.5 × Value(up) + 0.5 × Value(down)] / (1 + spot rate at Time 0) = [0.5 × 0.4209% + 0.5 × 0.0751%] / (1 + 3.0454%) = [0.21045% + 0.03755%] / 1.030454 = 0.248% / 1.030454 ≈ 0.2406% The calculated value of approximately 0.24% matches option B.
Author: LeetQuiz Editorial Team
Ultimate access to all questions.
An analyst gathers the following information about a 2-year European-style call option on the periodically compounded 1-year spot interest rate:
Call exercise rate 3.1000% Risk-neutral probability of an up move 50% 1-year spot interest rate at Time 0 3.0454% 1-year spot interest rate at Time 2 after two up moves occur 3.9706% 1-year spot interest rate at Time 2 after up and down moves occur 3.2542% Call option value at Time 1 when an up move occurs 0.4209% Call option value at Time 1 when a down move occurs 0.0751%
If the option is cash settled at Time 2 based on the observed rate, the option value as a percentage of the notional amount at Time 0 is closest to:
A
0.15%
B
0.24%
C
0.87%
No comments yet.