Interpreting Theta as Time-Passing PnL in FX Forwards

Summary

The document explains why an outright FX forward can have theta even though it has no option-style time value. It frames theta more broadly as the change in a position’s value when time advances while market inputs are held fixed. In an FX forward, this passage of time changes the remaining accrual and the discount factors associated with the two currencies, so the position’s net present value can change.

The discussion distinguishes this time-passing PnL from the forward points’ interest-rate sensitivity, while noting that the effects are related through discounting and accrual. It offers a conceptual explanation rather than a formula or worked example, and it does not quantify the size or direction of the effect for a particular trade. The exact theta measure can depend on convention and valuation setup, so the answer should be read as an interpretation of the term rather than a complete calculation procedure.

Key ideas

• FX theta can refer to the PnL from advancing time while holding market data fixed.
• An FX forward can have nonzero time PnL despite being a linear product.
• As time passes, changes in accrual and currency discount factors affect the forward’s value.
• This theta concept differs from option theta, though it is connected to forward valuation.

Tags

# What is FX theta in linear products?


# What is FX theta in linear products?












While I understand theta (time decay) in options, I often see theta being computed for linear products as well (outright FX forwards). What is theta in this case then? And how is it different from the interest rate sensitivity that comes from the forward points?

## Answer by Peaceful (score 4)

https://quant.stackexchange.com/a/48923

I think your FX theta is probably not the same as the theta in black scholes sense.

I think it may mean time pnl, which is applicable to all products, i.e., the PnL of time passing 1 day, but keeping all the market data the same. Note that here you have two markets, market 1 (original market) and market 2 (the original market's but moving 1 day forward)

For options, one part of time pnl would come from theta. For linear products, a part would come from the 1 day less of accrual.

## Answer by Daniel (score 0)

https://quant.stackexchange.com/a/83791

As you step through time the spot price and the interest rates on your respective curves stay constant ... This means that the discount factors on the two currencies must change. This change in discount factors changes the NPV of the trade. Thus the theta component of PnL is not zero.

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