Least-Squares Monte Carlo for American Call Options

# Can call options be priced with Least-Squares Monte Carlo?


# Can call options be priced with Least-Squares Monte Carlo?












I have been reading about Least-Squares Monte Carlo (using Longstaff & Schwartz algorithm) for option pricing. So far, I have only read examples that uses LSMC for american/bermudan PUT options only. Is there any reason for that? Or can LSMC also be used to price American CALLS? If not, then why not?

## Answer by Mark Joshi (score 5)

https://quant.stackexchange.com/a/25091

American calls on a non-dividend paying stock are worth the same as European ones so there is no point to using least-squares.

## Answer by Quantuple (score 1)

https://quant.stackexchange.com/a/25098

Mark Joshi's answer is totally correct. But I would appreciate to elaborate a little.

In textbooks you often read the exact same argument he pointed out to you.

In practice however, in the equities world, you almost always have to deal with dividends. So it is rather the American put which becomes similar to its European counterpart, and the American call which starts differing from its European parent.

This is especially true in the current low/negative rates environment. You can take any single stock option chain to check that.

So I would say it really depends on the market you are looking at. But anyways, yes, LSM can be used both for American puts and call (and even more complex payoffs such as Bermudan options).

Don't forget that it only produces a lower bound though. You can find more info in the brilliant papers of @Mark Joshi.

## Answer by Yian Pap (score 0)

https://quant.stackexchange.com/a/25193

Of course LSMC can be used in any case where you would benefit from early exercise (and the contract's not too convoluted I guess). So yes, if the Bermudan/American call is on a dividend-paying stock, then L-S could/would be used same way as for a put. But what happens if you try to price a Bermudan call without dividends with L-S? You should in theory get the European price as MJ is saying (even if there's no point doing it since we know this is what we should get anyway).

But has anyone tried that? I have, and in my experience L-S does not work very well in this case, in that it under-prices the option, giving a value markedly lower than the European price! The reason is, I theorise, the following: As we know L-S provides only an estimate of the continuation value and hence the decisions taken based on it will be sub-optimal and the prices low-biased. Now in the case of the American/Bermudan call with no dividends, even the slightest error in the continuation value fit will result in a sub-optimal exercise decision because the early-exercise premium is zero here. So based on the continuation value the algo should never lead to exercising in any of the simulated paths, but it actually does so we lose value...

When the dividend yield is non-zero but still pretty low, L-S also struggles and then as we increase the dividend yield and there's a clear early-exercise benefit, then it starts working better (just like it does with a Bermudan put without dividends), as in the valuations it produces are more accurate, i.e. less low-biased.