Upper Bound:

The price of a European put option cannot be higher than ₹833.50, which is the present value of the strike price. If the put option costs more than ₹833.50, say ₹860, you can make an immediate profit by:

• Selling the put option for ₹860

• Investing ₹833.50 at 8% interest to get ₹900 after 1 year

This results in a profit of ₹26.50 (₹860 - ₹833.50).

Key Points:

• The upper bound of a European put option is the present value of the strike price.

• The dividend on the stock does not affect the upper bound.

• The maximum loss for a put writer is the strike price, which can be reduced by investing in risk-free investments at 8% returns.

• A European put option cannot be equal to or higher than the present strike price.

Lower Bound of European Put Options

A put option's price cannot be lower than the difference between the present value of the strike price and the current stock price.

Example:

• Stock price: ₹70

• Strike price: ₹75

• Present value of strike price: ₹73

In this case, the put option's price cannot be lower than ₹3 (₹73 - ₹70). If it were, an investor could:

• Buy the put option

• Borrow money equal to the present value of the strike price (₹73)

• Use the borrowed money to buy the stock at the current market price (₹70)

• Make a profit

Summary of Upper and Lower Bounds:

Call Options:

• Upper bound: Cannot exceed the stock's value

• Lower bound: Cannot be less than the difference between the stock price and the present value of the strike price

Put Options:

• Upper bound: Cannot equal or exceed the present value of the strike price

• Lower bound: Cannot be less than the difference between the present value of the strike price and the stock price