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Q4ii) Paper B Apr22

S

sophieactrainee

Keen member
Hi there,

I am completing Q4ii) of Apr22 Paper B.

Change in derivative price is approximately

dp = delta dS + theta dt + rho dr

I am confused because for theta they use -0.175, and dt = 1 - 0 = 1, where did the negative come from? I calculated theta to be 0.175?

Thanks
 
Hi Sophie,

The theta is negative.

Theta is the rate of change of the derivative price in respect of t, which is the time since the start of the contract. Therefore, as t increases, your time to maturity decreases by that amount.

This means in your calculation of theta, if, say, you had changed the maturity by an amount x, this is equivalent to t changing by minus x, and therefore in your calculation you end up with theta as a negative number.

We can think of this conceptually as if t increases, there is less time for things to move in our favour, whilst the downside risk is capped. Therefore, this leads to a decrease in the value of the derivative and so theta is negative.

I hope this helps, please let me know if there are any followups.

Alvin.
 
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