# Call Accumulator Theta

Call accumulator theta describes the change in the fair value of a call accumulator due to a change in time to expiry, i.e. it is the first derivative of the call accumulator fair value with respect to a change in time to expiry and is depicted as:

#### $\Theta = \frac{dP}{dt}$

where P is the call accumulator fair value and t is time to expiry.

### Evaluating Call Accumulator Theta

Call accumulator Theta = Payout1 x Binary Call Option Theta(K1) + Payout2 x  Binary Call Option Theta(K2)

+ Payout3 x Binary Call Option Theta(K3) + Payout4 x  Binary Call Option Theta(K4)

where the terms to the right are the binary call option theta with strikes K1, K2, K3 and K4 respectively.

### Call Accumulator Theta Over Time

Call accumulator theta is displayed against time to expiry in Figure 1. The black 0.1-day profile shows the theta increasingly rising and plunging around zero as the increasing payouts take effect. With 25-day to expiry the profile is almost flat. The averaging of all four strike’s binary call thetas smooths the manner in which the fair value decays and appreciates.