Valuing a Call with a Two-Year Exercise Restriction

Summary

The document poses a valuation problem for a call option with a three-year life that cannot be exercised during its first two years, but may be exercised at any time during the final year. It supplies assumptions for the underlying price, strike, risk-free rate, and volatility, then asks whether a binomial tree is suitable or whether a Black–Scholes–Merton value is an adequate proxy.

Because exercise is permitted before expiration during the final year, this is an early-exercise feature rather than a standard European call. The document provides no answer, valuation, derivation, or comparison of methods, so it does not establish whether the proposed proxy is accurate. Its useful contribution is framing the option terms and identifying the modeling choice that needs to be resolved.

Key ideas

• The option has a three-year life and cannot be exercised during its first two years.
• Exercise is allowed at any time during the final year, making the timing feature relevant to valuation.
• The question contrasts a binomial tree with a Black–Scholes–Merton proxy.
• No valuation result or method comparison is provided.

Tags

# 64385


# Valuing a call option that is issued today, exercisable after 2 years from the issue date and expires 3 years after the issue date












if we assume:

Current price: $0.25

Exercise price: $0.25

life: 3 years

Risk free rate p.a: 0.2%

volatility p.a: 85%

The option cannot be exercised within the first 2 years, after 2 years, it is exercisable at anytime until expiry.

How would you value this? I initially thought a Binomial tree but then thought that BSM would probably be a close enough proxy given it assumes exercise at expiry.

Thoughts?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.