---
title: C13 PROPERTIES OF STOCK OPTIONS
description: "## FACTORS EFFECTING OPTION PRICES **Effect of increasing a factor on the price of an option:** ![](https://falconedufin.com/wp-content/uploads/2021/05/Picture14-300x201.png) ## LOWER & UPPER BOUNDS FOR OPTIONS ![](https://falconedufin.com/wp-content/uploads/2021/05/Picture15-300x161.png) Where,  c = value of European call option C = value of American call option…"
url: "https://falconedufin.com/book/%25knowledge_base%25/book-3-fmp/c13-properties-of-stock-options/"
updated: "2022-08-31"
category: Book 3 FMP
---

# C13 PROPERTIES OF STOCK OPTIONS

## FACTORS EFFECTING OPTION PRICES

**Effect of increasing a factor on the price of an option:**

![](https://falconedufin.com/wp-content/uploads/2021/05/Picture14-300x201.png)

## LOWER & UPPER BOUNDS FOR OPTIONS

![](https://falconedufin.com/wp-content/uploads/2021/05/Picture15-300x161.png)

Where,  c = value of European call option

C = value of American call option

p = value of European put option

P = value of American put option

## PUT CALL PARITY

Put call parity is the relationship that must exists between the prices  of **European**put & call option, having same underlie, strike price and expiration date.

** ****Call + Xe^- rT = S~0 + Put  **

|                       |

Fiduciary call      Protective put** **

## RELATIONSHIP BETWEEN AMERICAN CALL & PUT OPTION

Put call parity only holds for European option. For American options, we have an inequality.

**S~0 - X ≤ C - P ≤ S~0 - Xe^- r T**

## IMPACT OF DIVIDENDS ON OPTION PRICING BOUNDS

To prevent arbitrage, when a stock pays a dividend, its value must decrease by the amount of the dividend. This increases the value put & decreases the value of call.

**European option:**

c ≥ S~0 - D - Xe^- r T

p ≥ S~0 - D - Xe^- r T

**Early exercise of American option:**

P + S~0 = C + D + Xe^- r T

S~0- X –D ≤ C - P ≤ S~0 - Xe^- r T