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Donate Login Sign up Search for courses, skills, and videos. Call option as leverage. Put vs. Put-call parity. Put writer payoff diagrams. Call writer payoff diagram. Put-call parity arbitrage I. Put-call parity arbitrage II.
Put-call parity clarification. Option expiration and price. Next lesson. Current timeTotal duration Google Classroom Facebook Twitter. Video transcript If we want to get the upside of owning a stock while still mitigating the downside, in case the stock price goes down, we saw that we could buy a stock and an appropriate put option. So that when the stock goes below some price, the put option starts to have value, and so it mitigates our downside. And just as a review, these payoff diagrams are the values of-- or at least the one on the left, is the value of our holdings at some future date.
And we're defining that date to be the maturity date of the options under question. Now, and this one over here is the profit at that maturity date, and that's why we're subtracting the actual costs to enter the position on this one on the right. Now the question I want to answer in this video is how can we get the same payoff diagram without buying either stocks or puts? Knowing any two of S , C or P allows us to calculate the third.
Of course, the immediate use of this formula will be to combine the security price and the value of the call option from the solution of the Black-Scholes equation to obtain the value of the put option:. For the sake of mathematical completeness we can write the value of a European put option explicitly as:. Using the symmetry properties of the c. Now we use the Black-Scholes formula to compute the value of the option before expiration. Notice two trends in the value from this graph:.
We can also plot the value of the put option as a function of security price and the time to expiration as a value surface. This value surface shows both trends. This section is adapted from: Financial Derivatives by Robert W. Michael Steele, Springer, New York, , page The result can be plotted as functions of the security price as done in the text.
In particular, the calculation of d 1 and d 2 uses broadcasting, also called binary singleton expansion, recycling, single-instruction multiple data, threading or replication. R script for Black-Scholes pricing formula for a put option. Octave script for Black-Scholes pricing formula for a put option. Financial Derivatives. Institute of Finance, Michael Steele. Stochastic Calculus and Financial Applications.
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