Modified Theta

A

Amahrix

Modified Theta is the price of an option today using current volatility less the price of the same option tomorrow using the volatility of one day shorter option.

Above is the definition of Modified Theta in Dynamic Hedging (Nassim Taleb).

He goes on to say.. "It is usually interpolated using a square root of time method, to take into account the possible drop on the volatility curve".

With that being said.. may I request someone with some expertise to showcase to me an example of calculating the modified theta?

My thinking:

1. I get the price of an option today, such as TWLO 3 MAY 19 136 Strike BID: $7.70 VOL 132.34%
2. I don't understand the 2nd part of the equation.. "less(minus) the price of the same option tomorrow using the volatility of one day shorter option".

Peace,
Amahrix
 
Amahrix said:
2. I don't understand the 2nd part of the equation.. "less(minus) the price of the same option tomorrow using the volatility of one day shorter option".
More...
The implied volatility has some term structure, so as you are approaching expiration it's going to be pricing on a different implied vol. He assumes that you would calculate the term-structure adjusted implied vol using a variance interpolation. So "modified theta" is

price(t_expiration - tomorrow, iv_iterpolated) - price(t_expiration - today, iv_actual)

which to the first approximation can be expressed via greeks:

theta_mod = theta + vega * (iv_iterpolated - iv_actual)

Amahrix said:
1. I get the price of an option today, such as TWLO 3 MAY 19 136 Strike BID: $7.70 VOL 132.34%
More...
3rd of May is the very first expiration (this week). The time is so short that Vega pnl (which is what modified theta is all about) is kinda irrelevant :)

Scratch that (just saw the 7.7 price), at 150 vol vega is certainly a real deal :) No roll-down though, it's all vol fluctuation
 
Hi Sle,

I appreciate you taking your time out to respond to me.

Before I go over your response and try to understand everything..

sle said:
Scratch that (just saw the 7.7 price), at 150 vol vega is certainly a real deal :) No roll-down though, it's all vol fluctuation
More...

In what sense? A deal to the seller or buyer and why?

(p.s. I am short that strike and exp). I tend not to put myself with no time diversification but I deemed these prices a deal for shorting).

Peace,
Amahrix
 
It's that level of volatility is the going to be changing much faster than the roll-down. Modified theta is useful for things like SPX vol where daily fluctuations in the fixed strike volatility are comparable to the changes due to the slope of the surface.

Amahrix said:
(p.s. I am short that strike and exp). I tend not to put myself with no time diversification but I deemed these prices a deal for shorting).
More...
Didn't the stock just announce after hours with some crazy beat? A posteriori it looks like a great buy :D
 
You must log in or register to reply here.
Back
Top