# 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?

• If I understand you correctly, you have a 2x5 forward starting option of American flavor. You can check the Wikipedia page or this or this threads as a starting point. AFAIK the crucial point with these options is to determine an expectation for the asset price after 2 years; other than that Black-Scholes should suffice for Europeans (giving you at least a boundary for the American), but I'm not proficient enough to give a full answer Jun 4, 2021 at 6:29
• This is not a forward start option because the strike price is known on the issue date. This is a simple american call that can be exercised at any time between year 2 and year 3. In the absence of dividends it is optimal to exercise in year 3, so it boils down to a simple 3 years european call that can be valued using BS. Jun 4, 2021 at 7:07
• It can also be priced using the Binomial method: check Hull 8th ed C15: Employee Stock Options section Valuation for the theory. Jun 4, 2021 at 12:38