Valuing a Bear Put Spread by Pricing Its Component Puts

Summary

The document describes how to value a European bear put spread, including one embedded in a contingent value right. The position consists of a long put at the higher strike and a short put at the lower strike. Under the Black–Scholes framework, price each put separately using the underlying price, risk-free rate, volatility, and time to maturity, then subtract the short put’s value from the long put’s value.

The example identifies strikes of 175 and 150 and frames the instrument as a two-option portfolio. It does not provide the market inputs needed for a numerical valuation or work through the pricing formula. The approach therefore depends on suitable Black–Scholes assumptions and on having the remaining contract terms and market parameters; the brief answer does not discuss adjustments for dividends, early exercise, or the contingent right’s specific legal terms.

Key ideas

• A bear put spread combines a long higher-strike put with a short lower-strike put.
• The spread’s value is the long put value minus the short put value.
• Black–Scholes can price each European put using the relevant market inputs.
• A numerical valuation requires the underlying price, rate, volatility, and time to maturity.

Tags

# How would you do valuation of a bear put spread?


# How would you do valuation of a bear put spread?












I have a CVR (Contingent Value Right) that behaves as a European long put and short put, with strike prices of 175 and 150. It is possible to value this instrument by Black and Scholes?

## Answer by AdB (score 2)

https://quant.stackexchange.com/a/45525

As you write, a bear put spread is a combination of going long a European put with a higher strike (here, 175) and short a European put with a lower strike (here, 150). Given the remaining parameters in Black-Scholes, i.e. the current underlying asset price $S$, the risk-free rate $r$, the volatility $\sigma$ and time to maturity $T$, you can simply value the options individually using the Black-Scholes pricing formula.

The bear put spread is simply a portfolio of the two options, and hence its value is given by the value of the long put minus the value of the short put.

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