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A share is currently priced at 640p. A writer of 100,000 units of a one year European put option with an exercise price of 630p has delta-hedged the option with a portfolio which holds cash and is short 24,830 shares. The continuously compounded risk-free rate of interest is 3% p.a. and no dividends are payable during the life of the option. The assumptions of the Black-Scholes model apply.

Write down an expression for the delta of the option.

Calculate its value in this case.

Please help me out in this question I am unable to solve it. So far I tried differentiating option pricing formulae of black schole with S, price of share that will give me formulae for delta, right but how can we solve this equation without knowing volatility.This is where i am stuck.

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  • $\begingroup$ Since the writer of the option is delta-hedged, you only need to look at his hedge portfolio to infer the current delta. $\Delta = \frac{24830}{100000}$ $\endgroup$ – eltigrechino May 11 '15 at 14:43
  • $\begingroup$ Okie Thanx Got it $\endgroup$ – user53932 May 13 '15 at 10:44

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