Why Deep In-the-Money Puts Have Positive Vega

Summary

The discussion offers an intuitive explanation for why a deep in-the-money European put can retain positive vega, even when the underlying stock price is near zero. Its value includes time value as well as intrinsic value, and that remaining time value can respond positively to greater volatility. Higher volatility increases the chance that the put finishes out of the money, but it also increases the range of possible outcomes that may produce a larger payoff.

The answer frames the option’s limited downside for its holder against the possibility of substantial gains from favorable price moves. This intuition helps explain why the risk of becoming worthless does not necessarily outweigh the benefit of a wider outcome distribution. The response is qualitative: it does not derive the result, quantify the effects, or discuss how volatility surfaces, maturity, or other pricing assumptions influence vega.

Key ideas

• A deep in-the-money put can have time value in addition to intrinsic value.
• Greater volatility can increase that time value by widening the range of possible outcomes.
• Higher volatility also raises the chance that the put expires out of the money, so the intuition reflects competing effects.
• The explanation is qualitative and does not quantify vega or address model assumptions.

Tags

# Why Deep ITM European Put Options have positive vega?


# Why Deep ITM European Put Options have positive vega?












Could you explain, not from the perspective of B-S formula, but from intuition, why Deep ITM European Put Options have positive vega?

To take an example, if I have a European put options on a stock, and the stock price is close to zero, why does it still have positive vega? If the vol increases, wouldn't the stock price increase and the option price decrease?

## Answer by Ethantr (score 2)

https://quant.stackexchange.com/a/83749

I think one intuition can come from the distinction between the intrinsic value of an option and its time value. The deep ITM put option still has some time value, which is sensitive to a move in volatility.

I do agree however that this can be quite counter-intuitive as a higher volatility also means more chances to end up OTM or at least for the underlying asset's price to get closer to the strike. But even though the probability of the put option expiring worthless increases, the potential gains from favorable moves outweigh this risk : the loss is always limited to the premium paid for the option, while the potential gain of a put option can be substantial (and the potential gain of a call, theoretically unlimited but at least very large).

Does this point of view help ?

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