Put/Call parity to provide spot price

M

marameo

Suppose I want to calcuate IV and greeks for a long maturity option, like DEC14, I understand providing the current spot price in the bsm formula might turn out to be a bad idea. Also, consider there is not a DEC14 future trading, what can I do? I thought that maybe the option itself is pricing the correct underlying value. So, say I want to calculate greeks for a Call strike 5600 DEC14 european style (equity index) whereas I know the previously settlement prices for both the c5600 and p5600. Does it make sense to apply the p/c parity like this: 5600 +c5600 s.price - p5600 s.price to obtain the actual spot price to input in the bsm formula?

Thanks ever so much
 
Quote from marameo:

Suppose I want to calcuate IV and greeks for a long maturity option, like DEC14, I understand providing the current spot price in the bsm formula might turn out to be a bad idea. Also, consider there is not a DEC14 future trading, what can I do? I thought that maybe the option itself is pricing the correct underlying value. So, say I want to calculate greeks for a Call strike 5600 DEC14 european style (equity index) whereas I know the previously settlement prices for both the c5600 and p5600. Does it make sense to apply the p/c parity like this: 5600 +c5600 s.price - p5600 s.price to obtain the actual spot price to input in the bsm formula?

Thanks ever so much
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Yes it does. But if you back out the spot price using only one strike the price will be too inaccurate. The common practice is using all the strikes to find forward price (then you can calculate spot from forward). First, back out the implied forward price for each strike. Then find the weighted average where weights correspond to the volume of a synthetic market at a strike (that is the minimum of volumes for call and put market quotes).
You can use two approaches here:
1. Feed mid prices of calls/puts to back out mid forward price.
2. Take bid and ask separately and find bid and ask for a synthetic market. This is more precise as you will get best bid and best ask from different strikes. Then you will be able to find mid forward price based on synthetic market.
Once you got the forward price getting spot price is as easy as applying discount rate to your forward price. But I'd feed forward price to BSM directly, use Back model for futures (http://en.wikipedia.org/wiki/Black_model).

Let me know if I did not put it clear enough.
 
On the second thought, if your underlying pays dividends then using spot does not make sense. Just use forward price with Black model, it's safer.
 
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