Bounds for Option Prices
We will cover following topics
Introduction
In the world of financial derivatives, option prices play a pivotal role in determining the profitability of investment strategies. This chapter delves into the upper and lower bounds for option prices, providing insights into how these bounds contribute to understanding the potential values of options. By grasping these concepts, investors can make more informed decisions and evaluate the attractiveness of different option positions.
Upper Bound for Call Options
Call options grant holders the right, but not the obligation, to buy an underlying asset at a predetermined strike price. The upper bound for call options is the difference between the current price of the underlying asset and the present value of the strike price. In other words, it is the maximum amount an investor should be willing to pay for a call option. This upper bound is intuitive – if the option’s strike price is lower than the current asset price, the option would essentially provide an immediate profit if exercised.
Lower Bound for Call Options
The lower bound for call options is straightforward – it’s zero. Call options can never be priced below zero, as they represent a right and not an obligation. If the underlying asset’s price remains below the strike price, the call option’s value diminishes to zero at expiration. The holder can simply allow the option to expire unexercised, avoiding any additional loss beyond the initial premium paid.
Upper Bound for Put Options
Put options provide holders the right to sell an underlying asset at a predetermined strike price. The upper bound for put options is the strike price itself. This is because, in the event that the underlying asset becomes worthless, the put option holder can exercise the option to sell the asset at the strike price and lock in that value.
Lower Bound for Put Options
The lower bound for put options is linked to the concept of arbitrage. If the put option’s strike price is higher than the current value of the underlying asset, an investor could simultaneously buy the asset in the market and exercise the put option to sell it at a higher price. This risk-free profit opportunity prevents the put option price from dropping below the intrinsic value of the option, which is the difference between the strike price and the current asset price.
Considering Dividend-Paying Stocks
Incorporating dividends into the option pricing framework requires adjusting the bounds accordingly. Dividend payments can affect the option’s value and its upper and lower bounds, particularly if they are expected to occur before option expiration. Dividends reduce the value of the underlying asset and, consequently, influence the bounds for both call and put options.
Conclusion
Understanding the upper and lower bounds for option prices provides investors with a solid foundation for evaluating the fair value of options. The upper bounds represent scenarios where options could provide immediate profit opportunities, while the lower bounds underscore the limitations of option values. Incorporating dividend payments into these bounds further enriches the analysis, allowing investors to make more nuanced decisions when trading options. By grasping the concepts of option bounds, investors can navigate the complex world of derivatives with greater confidence and insight.