Risk-free return has been at the core of option pricing models. A number of things follow from it, such as the put-call parity. What if there is default on bonds? Are there are flaws in option pricing models? For instance which side is better: the short call or the short put? We know what the crowds in here have been saying, but could we make a review?
Are There Flaws In Options Pricing?
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Your cost of capital, not risk free return is only one input into option pricing. And, unless your trading longer term options, normally the input in the model that is the easiest to value. That said, if you believe interest rates will rise quickly, you would want to put on reversals in leaps. Positions that receive short stock interest rates rebates would benefit from higher rates. So, in general, short put hedged positions would be better than short calls.
Very few readers in this forum will benefit from this strategy. You would have to have a relationship with a prime broker that offers short stock rebates at close to fed funds. I would think there is a better way to profit from a default.
The risk-free rate (which is misnamed, it's really the perceived-as-least-risky rate) is just another input to the pricing models. If you think people are under- or overestimating it, you can plug in your own and generate your own fair-value price.
There are all sorts of flaws, including the use of the "risk-free rate" shortcut. In reality, as mentioned above, it should always be based on the marginal funding rate, rather than some particular mkt rate. There are all sorts of other drawbacks, but they don't invalidate the theory.
Of course there are flaws in options pricing, and there always will be.
The reason is that in order to price an option(or any derivative for that matter), one has to start with a model for the underlying. Truth be told, no one really knows what the right model is or even if a "right" model exists.
In any event, the issue with the risk free rate is not really at the core of option pricing, lack of arbitrage is.
The reason is that in order to price an option(or any derivative for that matter), one has to start with a model for the underlying. Truth be told, no one really knows what the right model is or even if a "right" model exists.
In any event, the issue with the risk free rate is not really at the core of option pricing, lack of arbitrage is.
In order to determine a "fair value" for an option, you have to first assign a probability to each possible outcome. Which is to say that if you're pricing an option on IBM, you have to determine the probability that IBM will be at each possible price at expiration. What is the probability it will be at 180? Or at 181.27? Or at 192.11?
In other words, you have to choose a probability distribution. The convention has been to assume a lognormal probability distribution ever since Black and Scholes demonstrated in 1974 that it is mathematically acceptable to do so.
But is the lognormal probability distribution really a perfect reflection of reality? Of course not.
You can make of that what you wish. Warren Buffett a few years ago looked at the fact that the DJIA had risen from about 40 in 1932 to about 14,000 in 2000 and decided the "random walk" assumption for stocks is absurd and that OTM puts priced under a random walk assumption are way overpriced. He put his money where his mouth was, and sold some several billion dollars worth of FOTM SPX long-term puts. Time will tell if he was right or wrong.
Put-call parity doesn't "follow" from and doesn't depend on the validity of the risk-free rate of return.
You are right that put call parity doesn't follow from the validity of the risk free rate, it follows from no arbitrage.
However, the argument does hinge pretty heavily on the existence of some form of safe investment of capital. If the economy were in a truly horrible state at which there was some sort of nontrivial probability of default on even the so called safest bonds, one would need to re-think the put call parity argument. The replicating portfolio would no longer stay positive with probability one.
To be clear, you seem to be referring to the physical(or true) probabilities here. That is fortunately not something you need to know to price an option. The only thing you need to know about physical probabilities is which events have probability zero. For the purpose of pricing, you need only the risk neutral probabilities(i.e- the probabilities of the above events if we suppose that all stocks are growing instantaneously at the risk free rate, and are only distinguished by other distributional factors, such as variance)