How Early Exercise Can Leave a Dealer Short an Out-of-the-Money Put

Summary

The document gives two examples of how exercising an in-the-money American option can change a dealer’s remaining exposures. In one setup, the dealer holds a deep in-the-money American put and is short a European put at the same strike and expiration. Exercising the American put leaves the short European put and a short stock hedge; put-call parity makes that combination equivalent to being short a call at the strike.

A second example starts with a long in-the-money call hedged by a short out-of-the-money put and short shares. Ahead of an ex-dividend date, exercising the call provides shares that offset the short stock, leaving the short put. These are illustrative position decompositions, not a general rule for every dealer book. The outcomes depend on the starting hedge, option style, strike and expiration alignment, and in the second example, the dividend-related timing and share netting. The source offers scenarios but no market data or empirical evidence about how often they occur.

Key ideas

• Exercising an American option can alter a dealer’s combined option and stock exposure.
• A short European put paired with short stock can be represented as a short call through put-call parity.
• Exercising a long call can provide shares that offset a short stock hedge.
• In the stated dividend example, that share offset leaves the dealer short an out-of-the-money put.

Tags

# Dealers becoming synthetically short an out-of-the-money option


# Dealers becoming synthetically short an out-of-the-money option












> "When dealing with a large-size position, dealer, upon exercise, synthetically become short an out-of-the-money option."

How does this work, I cannot see why this happens synthetically in particular?

## Answer by dm63 (score 3, accepted)

https://quant.stackexchange.com/a/24885

Here's one scenario: dealer is long a deep in the money American put (say strike is K and the current stock price is S < K ), versus being short a european put with the same strike and final expiration. If the dealer exercises early the American put, he is now short the European put at K with a short stock hedge against it. Thus he is synthetically short a European call struck at K. ("synthetically" via put-call parity). I'm not sure if that's what is being referred to.

## Answer by onlyvix.blogspot.com (score 2)

https://quant.stackexchange.com/a/24895

Here's the example of what is in the quote: dealer is long an ITM call. As a hedge the dealer is also short OTM put (with the same strike) and short stock. This is a "riskless" position, equivalent of a bond.

The underlying pays a dividend, and a day before the ex-date dealer exercises the call. The shares that dealer received from exercise are netted against his existing shorts to zeros, which leaves the dealer short an OTM put.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.