# Lower bound of the put option price. Option valuation: Upper bounds and lower bounds – Part 1 | Basics of Share Market

Tweet What are upper and lower bounds of options? One important principle while valuing options is that at any time, the value of a call or a put cannot exceed certain limits — on the higher side as well as on the lower side.

These maximum limits will have to be discussed for European and American options separately.

We first take up the upper and lower bounds of European calls. In such a scenario, anybody can write the call and sell the stock on spot, and take home the difference of 5 per share.

Identify and compute upper and lower bounds for option prices on non-dividend and dividend-paying stocks. Explain put-call parity and apply it to the valuation of European and American stock options, with dividends and without dividends and express it in terms of forward prices. Explain and assess potential rationales for using the early exercise features of American call and put options.

Dividend, when paid, decreases the value of shares to that extent. Hence on expiry, the stock will be valued at 45 50 — 5 in the spot market and logically, the call value cannot exceed 45 per share.

This brings us to the first principle in option value — the upper bound value of an European call can never rise beyond the value of the underlying stock.

### Lower Bound for the price of a European Call option 《Nasrin Sultana》

When the dividend is known with certainty, the call values cannot rise beyond the spot value of the stock less present value of the dividend.

Lower bounds of European call values: What would be the lowest value for an European call?

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It should be zero. Lower bound of the put option price cannot fall below that, Right?

For the call value to be at zero, the stock value should also fall to zero. If the stock value is above zero say 2 the minimum value of call should be the present value of Rs 2 strike price. One year European option call at strike price is available. In this case, the value of the call cannot fall below 2 — If it falls to say, Re 1 then — You can buy the call at strike — you pay Re 1 You sell the stock at — You get Use that to exercise the call and get back your shares.

This lesson is part 2 of 6 in the course Option Valuation Lower Bound We know that the value of an option is equal to the sum of its intrinsic value and time value. Since an option cannot sell below its intrinsic value, its value cannot be negative, Therefore, the lower bound for both American and European options is zero. Upper Bound Call Options A call option provides the option buyer the right to buy the asset. For the option to have value, its price at any time must be lower than the underlying stock price at any time. This is because if the option price were higher than the stock price, it would be cheaper to just buy the asset directly in the spot market.

Get a profit of Rs 1, risk free — immediately. May be that was slightly confusing. As a next step, here also, we need to discus the effect of dividends.

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The dividend to be received a year later is estimated at Rs 5 per share. When the dividend is known with certainty, the call values cannot fall below the spot value of the stock minus present value of the dividend minus present value of the strike value.

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