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noexpert
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Joined: April 27th, 2007, 2:20 pm

Constant Volatility Vs Normally drawn volatility

November 1st, 2007, 10:49 pm

You have to price a call option either with a constant volatility say (15%) or by drawing volatility from a normal distribution with mean 15%. Which option would be expensive? Can it be proved mathematically?
 
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tuchong
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Constant Volatility Vs Normally drawn volatility

November 2nd, 2007, 1:27 am

How can a volatility be normally distributed? (\sigma > 0)
 
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rcyeh
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Constant Volatility Vs Normally drawn volatility

November 8th, 2007, 2:37 pm

Are you saying that in both cases the volatility would be constant during the life of the option, but in one case the volatility is known and in the other case, we are finding the expected price of the option given that the volatility is from a distribution centered at the known value?If so, I would pay more for the latter option. Suppose the price of an option is convex with respect to volatility. Then we can use Jensen's inequality.
 
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noexpert
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Constant Volatility Vs Normally drawn volatility

November 25th, 2007, 12:39 am

Thats correct rcyeh ! Jensen's inequality !
 
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amit7ul
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Constant Volatility Vs Normally drawn volatility

November 27th, 2007, 5:35 am

volatility being negative is not a problem.. atleast in BS as there is no need to take its root in BS pricing formulas and in spot evolution its coefficient of weiner innovation. infact C(sigma)=P(-sigma), sigma>0.. so if noexpert's question was supposed to be a teaser then jensen is the straightforward answer.but if it was an interview question for RnD job then ???
 
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QuantumHallEffec
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Constant Volatility Vs Normally drawn volatility

October 15th, 2010, 7:42 pm

"Suppose the price of an option is convex with respect to volatility", one the contrary, for at or near the money call option, volga is negative. So the option price is a conacave function of vol.