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- 7/19/11
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Hello!
I want to discuss what is the most reasonable way to model historical option prices when you only have daily prices of the underlying and the implied vols. It is the first time I'm doing something applied in mathematical finance, so please bear with me
Let's make an example out of it. Consider a 1 week call option on a stock index. The option is initialized on a Monday and expires on Friday. Just to be clear about the setting, we have the index closing price and the implied vols for Monday, Tuesday, Wednesday, Thursday and Friday. I let Monday's closing price represent the price on Monday. If we think about the theory and a continuum of prices it's like a piecewise constant price process.
So when a contract with moneyness 105% is initialized on Monday, the strike price will be 1.05*[closing price on Monday]. And on Tuesday one should use the closing price on Tuesday etc. So there is no change in the prices during the days, but rather between the days, which is kind of confusing theoretically but (at least I think so) the most reasonable way to use discrete data.
On the Friday we get a situation where we first use the closing price of the index to get the option price with 1 day left to maturity and then again for the settlement price which would be min(closing price minus the strike, 0).
An alternative way, that I also taught of was to let one day's closing price represent the next day. So the closing price on Thursday will be used to represent the price on Friday and the closing price on Friday will be used to calculate the settlement price. But then we get problem when is comes to initializing the option. Should one then use the closing price from the previous Friday? Which way is most reasonable?
I'd appreciate your input
Thanks in advance!
/DT
I want to discuss what is the most reasonable way to model historical option prices when you only have daily prices of the underlying and the implied vols. It is the first time I'm doing something applied in mathematical finance, so please bear with me

Let's make an example out of it. Consider a 1 week call option on a stock index. The option is initialized on a Monday and expires on Friday. Just to be clear about the setting, we have the index closing price and the implied vols for Monday, Tuesday, Wednesday, Thursday and Friday. I let Monday's closing price represent the price on Monday. If we think about the theory and a continuum of prices it's like a piecewise constant price process.
So when a contract with moneyness 105% is initialized on Monday, the strike price will be 1.05*[closing price on Monday]. And on Tuesday one should use the closing price on Tuesday etc. So there is no change in the prices during the days, but rather between the days, which is kind of confusing theoretically but (at least I think so) the most reasonable way to use discrete data.
On the Friday we get a situation where we first use the closing price of the index to get the option price with 1 day left to maturity and then again for the settlement price which would be min(closing price minus the strike, 0).
An alternative way, that I also taught of was to let one day's closing price represent the next day. So the closing price on Thursday will be used to represent the price on Friday and the closing price on Friday will be used to calculate the settlement price. But then we get problem when is comes to initializing the option. Should one then use the closing price from the previous Friday? Which way is most reasonable?
I'd appreciate your input
Thanks in advance!
/DT