When Negative Strike Prices Make Sense for Options

# Can strike prices of options be negative?


# Can strike prices of options be negative?












I am trying to understand the stochastic model of a financial market in one period by [Föllmer, Schied]. They introduce call and put options for the primary assets, which are non-negative. They do not specify if the strike can be negative or if it should be positive. I think its economically not useful to have negative strike prices for options whose underyling is one of the primary assets. Since $(S -K)^+>0$ for $S\ge 0$ and $K<0$ it would be basically a sure payoff. Is this a fair assessment?

Next, they define basket options, whose underyling is the value of some portfolio. Some portfolio can have negative inital value. Thus, I believe that it could be useful to have a negative strike price. Is this true?

Wikipedia page on strike prices does not specify it either.

I can specify the model if necessary. Let me know. Thanks for reading.

## Answer by D Stanley (score 5, accepted)

https://quant.stackexchange.com/a/50391

If the underlying asset cannot be negative, then an option on it with a negative strike would be meaningless. A call would always be in-the-money with no chance of being worthless, and a put would always be worthless.

You can, however, have options on assets that can have negative values, like interest rates (a relatively recent phenomenon), or spread options, more common in commodities like WTI-Brent.

Note that the payout formulas are the same - if you have a spread call option with a strike of -2, the payout would still be $\max{[(S-K),0]}$. If the spread was, say, -1, then your payout would be $\max[({-1} - {-2}),0] = 1$. If the spread were -3, the payout would be $\max[({-3} - {-2}),0] = 0$.

The models for pricing these options are different, however, since the standard Black-Scholes model assumes an always-positive underlying price and log-normal rates of change.

## Answer by roz (score 3)

https://quant.stackexchange.com/a/50393

If your underlying can not take negative values then an option with a negative strike would be a sure payoff. There is however no reason preventing the option from having a negative strike. Id be happy to buy many such options from you.

## Answer by user42108 (score 2)

https://quant.stackexchange.com/a/59797

In addition to some outrights having negative prices (as pointed out by CasusBelli and discussed in a JPM piece from 2011), spreads can take negative values and options on spreads trade (e.g. CSOs in CL).

## Answer by CasusBelli (score 1)

https://quant.stackexchange.com/a/59796

I've heard of OTC options with negative strikes in electricity markets. If you have a lot of generation from non-intermittent sources, like hydrological and nuclear, negative prices are almost inevitable during periods with little demand.