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list1
Posts: 1696
Joined: July 22nd, 2015, 2:12 pm

### Unhedged options thought experiment

The question is about how we value the respective positions of the option and the trading (=delta1) desks. /// The original question was about that the Black Scholes formula is inappropriate in the case where assets are illiquid.So, moving to the valuation of the trading desk position. I claim this will be the sum of realised and unrealised P/L /// it is not clear what does it mean realised and unrealised and to what issue it related

complyorexplain
Topic Author
Posts: 93
Joined: November 9th, 2015, 8:59 am

### Unhedged options thought experiment

QuoteOriginally posted by: list1The question is about how we value the respective positions of the option and the trading (=delta1) desks. /// The original question was about that the Black Scholes formula is inappropriate in the case where assets are illiquid.So, moving to the valuation of the trading desk position. I claim this will be the sum of realised and unrealised P/L /// it is not clear what does it mean realised and unrealised and to what issue it related And I have argued that the BS formula is perfectly appropriate. This is because the trading desk position should be value at zero at inception. And given that the option desk position will be reasonably hedged, BS will give an approximately correct value. Since the sum of the position values is the BS value, the BS value is correct.Realised and unrealised applies to the trading desk position. At inception, the P/L is zero. As the reference rate rises, there will be unrealised p/l. If any position is sold, there will be realised P/L. Remember that any p/l earned by the trading desk is exactly offset by the delta hedge p/l of the option desk. This will in turn be offset by the (unrealised) p/l on the option itself. ---- E.g. suppose the trading desk p/l on day two is £30. This will exactly offset a loss of £30 by the option desk on the opposite side of the hedge. But, assuming the option desk has estimated the volatility correctly, the option should have risen in value by £30. Thus, trading desk p/l is £30, option desk p/l is zero. Firmwide p/l is £30, because the firm as a whole has sold a put option and the underlying has gone up.Conclusion: Black Scholes gives the correct value.
Last edited by complyorexplain on May 18th, 2016, 10:00 pm, edited 1 time in total.

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