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Does inflation have any effect on options prices? If inflation increases, what will happen to the prices of puts and calls? My guess is that higher inflation will lead to higher interest rates, and higher interest rates will somehow affect the prices of options, but I'm not exactly sure how.

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Interest rates do have a mild effect on option prices since the value of the option is partly determined by the present value of the payoff in the future, and higher interest rates lower that present value.

But, inflation does not directly affect interest rates. There is some correlation, but inflation is a very broad measure of the prices of goods and services. It is not directly caused, and does not directly affect, interest rates.

Depending on the underlying asset, it's possible that inflation has a larger effect on that (and in an opposite direction) than the secondary affect it would have through interest rates.

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  • "it's possible that inflation has a larger effect on that ... than the secondary affect it would have through interest rates." — What does "that" refer to?
    – Flux
    Sep 4 at 5:44
  • "that" == "the underlying asset". For example, if you were looking at an option on an airline, inflation could have a larger impact on the stock price than the indirect effect through interest rates,
    – D Stanley
    Sep 5 at 20:05
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You can play around with the risk-free interest rate to see how it affects the pricing of options according to the Black-Scholes model here: https://www.wolframalpha.com/input?i=black+scholes

The risk-free interest rate is the rate you could get on US Treasuries over the duration of the option. It is closely related to inflation, though by no means identical. Either via Black-Scholes or intuitively, you can see that a higher interest rate means call options get more expensive and put options become cheaper: if I buy a one-year call option today with, say, strike equal to spot, then that's far more valuable than in would've been in 2019 insofar as the strike's real value will shrink much faster now that inflation has increased. Exactly the opposite applies to puts: it's less exciting to get to sell somebody a stock for $50 in a year than it would've been in 2019, since the difference between $50 now and in a year is larger this year than it was in 2019.

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Options prices are not affected by inflation. However, if interest rates are increased because of inflation, then option premiums will increase modestly because of the higher carry cost (risk free rate):

  • Call options have positive Rho, so as interest rates increase, call options tend to increase slightly in price.

  • Put options have negative Rho, so as interest rates increase, put options tend to decrease slightly in price.

It's possible that such option-speak is meaningless to you so let's try another way.

Put and call premiums are related by an arbitrage called a Conversion. The formula is:

  • Strike - Stk + Call - Put + Dividend - Carry Cost = 0

To make things easier to visualize, let's assume that the stock equals the strike price and let's factor. Then:

Call + Dividend = Put + Carry Cost

The takeaway from this equation is that put price increases, relative to the same series call by the amount of the dividend. And call price increases, relative to the same series put, by the amount of the carry cost.

Or simplifying even more, assume no dividend:

Call = Put + Carry Cost

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