The risk neutral probability of price, ^(pai), captures the probability of the price of the underlying increasing. As ^(pai) increases, the likelihood of the put option ending up in the money decreases.
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The risk-neutral probability of price, ^(pai), is a concept used in financial modeling, particularly in option pricing theory. It represents the probability that the price of the underlying asset will increase.
In option pricing, it is common to assume a risk-neutral world where the expected return on all investments is the risk-free rate. This assumption allows us to price options by discounting the expected future payoffs at the risk-free rate.
Now, let’s consider a put option, which gives the holder the right to sell the underlying asset at a specified price (the strike price) on or before a predetermined date (the expiration date). The put option is “in the money” if the price of the underlying asset is below the strike price, as the holder can sell the asset at a higher price in the open market.
The likelihood of the put option ending up “in the money” depends on the probability of the price of the underlying asset decreasing. Since ^(pai) represents the probability of the price increasing, the statement suggests that as ^(pai) increases, the likelihood of the put option ending up “in the money” decreases.
In other words, if the risk-neutral probability of price, ^(pai), is high, it implies that the market expects the price of the underlying asset to increase significantly. As a result, the likelihood of the price falling below the strike price and the put option becoming profitable decreases. Therefore, higher ^(pai) decreases the likelihood of the put option ending up “in the money.”