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2010-06-20
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Suppose the following information is provided for a new type of stock option.Estimate the 1-day theta in Black-Scholes model.

Stock Price (S) = 100
Option Price (V) = 10
Interest Rate (r) = 10%
Volatility = 50%

Delta = 0.5
Gamma = 0.02

(象徵性賞一幣, 先答對者得, 要簡單解釋)
(如題目有問題, 則賞指出問題者)

難易度: 1-2 吧?

最佳答案

lingyw04 查看完整内容

......The PDE form of BS formula. theta+0.5*(sigma^2)*(S^2)*gamma=r*(V-delta*S)
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2010-6-20 21:07:02
oddsmaker 发表于 2010-6-21 16:49
Can you elaborate what BS formula you refers to?
......The PDE form of BS formula.

theta+0.5*(sigma^2)*(S^2)*gamma=r*(V-delta*S)
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2010-6-22 04:39:47
0.0575

Theta can be computed by B-S formula, given all the B-S conditions are satisfied and this is a European option. The annualized theta in this case is 21, then divided by 365 to get the 1-day theta. Correct?
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2010-6-22 05:49:01
Can you elaborate what BS formula you refers to?
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2010-6-23 02:44:35
good,
however normally there are 252 trading days per year.
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2010-6-23 04:38:00
tianjinxtl 发表于 2010-6-22 13:44
good,
however normally there are 252 trading days per year.
I am not sure. Actually, I have thought about that.

But since by replication, we set delta equal to the partial derivative of V w.r.t S, then the whole portfolio will accumulate at the risk free rate r.
When calculating the accrual interest rate, we don't differentiate business days with holidays, do we?
So, I still decide to normalize theta with 365.
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