Answer: put option and the value of a call option on the underlying will increase.

## Explanation In option pricing theory, volatility is a key determinant of option value. According to the binomial model and other option pricing models (like Black-Scholes), both call and put options benefit from increased volatility. ### Key Concepts: 1. **Volatility and Option Value**: Options give the holder the right, but not the obligation, to buy (call) or sell (put) an underlying asset at a specified price. Higher volatility increases the probability that the option will end up in-the-money. 2. **Asymmetric Payoff**: Options have asymmetric payoff structures - limited downside (premium paid) and potentially unlimited upside. Increased volatility increases the potential upside without increasing the downside risk. 3. **Binomial Model Perspective**: In the binomial model, higher volatility means larger up and down movements in the underlying asset price, which increases the range of possible outcomes and thus increases the expected value of both call and put options. ### Why Other Options are Incorrect: - **Option B**: Incorrect because both put and call options increase in value with higher volatility, not just puts. - **Option C**: Incorrect because both put and call options increase in value with higher volatility, not just calls. ### Additional Insight: This relationship holds true for both American and European options, and is a fundamental principle in option pricing. The only exception might be deep in-the-money options where the time value component is minimal, but even then, increased volatility generally increases option values. **Correct Answer: A** - Both put and call option values increase when volatility increases.

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