無聊中....出條題目給大家玩玩

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?

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)

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?

Can you elaborate what BS formula you refers to?

good,
however normally there are 252 trading days per year.

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.

The answer is correct.
The value is a bit different from mine, but it's not important.

1) I think divided by 365 is a more common practice, like interest rate.
2) FYI, the theta become upper bound if it's an American option.

It's the first time I used this "giving coin away" post function.
Please let me know if you haven't got the coin.

Thanks again for interest in the question.

The value is not important compared to how to solve. I don't really mind about that.

Trader convention does not mean everything.

I remember Bloomberg and Reuters pricer give "original" theta value.
I forgot the 1-day value is divided by 250 or 360, though I think it's 365.

oddsmaker 发表于 2010-6-23 05:18
The value is not important compared to how to solve

that's pure academic crap
if the number is wrong, it's wrong, you lose money, and your boss yells at you and you are fired, nobody cares how you solve it and why you get the  number wrong