Stratégies Options - At The Money Forward Relationships 1

" At the money forward " ATMF, that is when the strike is at the level of the forward, some particularly interesting relations appear.

When the strike is at the level of the forward, the option is At the money "forward" and the relations between delta and premiums allow to grasp intuitively option values very quickly

I - At the money forward

By definition, an option of European style) can be exercized only at maturity. According to the call - put parity, we know that European options aren't priced in fact on the spot, but on the forward. This element is moreover very present in the typical pricing models such as Black and Scholes.

Why ATMF ?
By choosing an ATMF option, we erase the interest rate influence on it. It allows afterward to argue as if the interest rates were zero. Relations will then be always true for any interest rate since the strike would be then adjusted.

a - A first remarkable element, is that call and put values are similar, on the other hand, deltas are different.

Example
If the underlying is set at 100 and we make interest rates varying from 0% to 5 %, and from 5% to 10 %, although strike and forward are the same, premiums, calls and puts, remain identical.

b - A second remarkable element due to interest rate variations involves variations only on the theta. Vega, gamma and delta remain the same.

II - Relation between delta and premium

An important relation between delta and premium can be considered when the option is ATMF.
At this level there, as r=0, we have:

Hence,

It is thus extremely easy to know an ATMF call value knowing only its delta.
Conversely, if we look for a particular delta ATMF without knowing either the maturity or the volatility, we find easily the value of this call.

How to use it :

→ A delta 0.6 ATMF for a spot at 100, means a call of 2*100 * (0.6-0.5) = 200*0.1 = 20

→ A delta 0.55 ATMF for a spot at 100, means a call of 2*100 * (0.6-0.5) = 200*0.05 = 10

It isn't needed to know expiry in order to price an ATMF option using its delta !

Next : At The Money Forward Relationships 2
Previous : Call-Put Parity : American Style Issue

Relationships Between Option Sensitivities - INDEX Relationships Between Option Sensitivities - CHAPTER I
Relationships Between Option Sensitivities - CHAPTER II
Relationships Between Option Sensitivities - CHAPTER III

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