Pricing Stock Options with Futures-Style Premium Settlement

Summary

The document asks how to price options on stocks when the premium is settled daily rather than paid upfront. It proposes adapting standard Black–Scholes pricing by multiplying the ordinary option value by the growth factor for the risk-free rate over the option’s life, drawing an analogy with futures-style settled options on futures. It also suggests deriving the Greeks from the adjusted price.

The text presents this as a question, not a verified result: no answer, proof, or numerical comparison is included. Whether the adjustment applies depends on the precise settlement and margining convention, cash-flow timing, and the pricing measure used. The proposed formula should therefore be treated as a hypothesis requiring derivation under the contract’s settlement rules, rather than as a generally established pricing result.

Key ideas

• The document distinguishes upfront-paid options from options whose premium is settled over time.
• It proposes adjusting a stock-option price by a risk-free growth factor, based on an analogy with futures-style options.
• The proposed formula and resulting Greeks are not validated within the document.
• Pricing depends on the contract’s settlement convention and the timing of cash flows.

Tags

# Future-Style settled options on stocks


# Future-Style settled options on stocks












I am trying to price future-style settled options on stocks (not on futures). I have researched about it but I can only find pricing for future-style settled options on futures, like in the following paper:

https://onlinelibrary.wiley.com/doi/abs/10.1002/fut.3990100402

Attempt for solution

My thought was to follow the idea about future-style settled options on futures. In such products, the premium is not paid up front, but it is settled on a daily basis. Thus, technically one does not need to discount the price. As a result, one can deduce the price of such products by multiplying the Black-Scholes on futures equation (otherwise known as Black's model) by $e^{rT}$ and one has:

$$P_{call}=FN(d_1)-XN(d_2)$$

So, with the same line of thinking, to calculate the price for options on stocks, one can take the normal Black-Scholes equation and multiply it by $e^{rT}$:

$$P_{call}=Se^{rT}N(d_1)-XN(d_2)$$

From this one can then calculate the greeks.

Is my thought correct? Can one deduce the future-style settled options on stocks like this?

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