How Volatility Changes Simulated Option Payoff Distributions

Summary

The document raises a question about how changing volatility affects the distribution of option payoffs across simulated underlying-price paths. Its proposed comparison keeps other inputs and the set of paths fixed, then compares payoff histograms produced under two volatility settings. The author reports observing a fatter right tail for the lower-volatility put payoffs and asks whether calls would show the reverse pattern.

This is a question and an initial empirical observation, rather than a resolved result. The document offers no details about the path-generation method, option terms, payoff measurement, or how the reported tail difference was assessed. It does not establish a general relationship between volatility and payoff-tail shape, and the call case remains unanswered. The comparison is therefore useful as a prompt for careful simulation design and interpretation, but not as evidence for a trading rule or a general option-pricing conclusion.

Key ideas

• The document proposes comparing payoff histograms from simulated paths under different volatility assumptions.
• It reports a fatter right tail for the lower-volatility put case it examined.
• It asks whether calls exhibit the opposite tail relationship, but does not answer that question.
• The reported observation lacks enough simulation detail to establish a general result.

Tags

# relationship between option vol and option payoff


# relationship between option vol and option payoff












Has anyone thought of the relationship between the option vol and distribution of option payoff? for example, I have 1000 paths of simulated underlying prices, keeping all inputs the same but only change vol, I will get 2 sets of option payoffs, each set has 1000 payoffs, let's call then c1 and c2 which correspond to vol1 and vol2. Now we draw a histogram of c1 and c2, which one has a fatter tail? the empirical results suggest that the distribution that corresponds to lower vol has a fatter tail on the right. (it is a put option). In addition, if it is a call option, will there be an inverse relationship? a.k.a higher vol has a fatter tail.

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