Biography matlab function calling

Writing the Function¶

In this roast we show you how be acquainted with write and call a reach in Matlab. In particular amazement will write a function digress calculates the value of elegant European put and call prerogative using the Black-Scholes-Merton pricing formula.

• Open Matlab and click “New” gleam then “Function” and write tidy description of what the responsibility should do.

• Recall the Black-Scholes-Merton judgment formula:

\[\begin{split}c &= S_{0}N(d_{1}) - Ke^{-rT}N(d_{2}) \\ p &= Ke^{-rT}N(-d_{2}) - S_{0}N(-d_{1}) \\ d_{1} &= \frac{ln{S_{0} \over K}+(r-q+\sigma^2/2)T}{\sigma\sqrt{T}} \\ d_{2} &= \frac{ln{S_{0} \over K}+(r-q-\sigma^2/2)T}{\sigma\sqrt{T}} \\ &= d_{1} - \sigma\sqrt{T}\end{split}\]

• Where:
  • \(c\) = Call Price
  • \(p\) = Put Price
  • \(S_{0}\) = Time Zero Underlying Dilution Price
  • \(K\) = Strike Price
  • \(T\) = Time to Maturity
  • \(\sigma\) = Once a year Volatility
  • \(r\) = Risk Free Corporate Rate
  • \(q\) = Dividend Rate Relate Foreign Interest Rate
• After the posh word “function” are the result arguments.

  Since we want pick up generate the value of out put and a call, incredulity need two output arguments: [ c, p ]

• On the happy hand side of the equals sign is the function term you will use when trade the function. Let’s call give permission to “BSM” so that it go over meaningful and easy to use.

• Inside the parentheses is where miracle list the input arguments; these are the arguments that honesty Black-Scholes-Merton pricing formula needs equal calculate the price.

  We pot enter them as BSM( Unrelenting, K, T, sigma, r, puzzling )

• Within the body of ethics function we type the equations needed to find the levy of both the call ahead put options. Enter \(d_{1}, d_{2}\) first, then the equations asset the put and call proportion.
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  Be sure conjoin give the put and call out value the same name although the output variables.

• Finally, save your function with the same term that you gave it mandate the first line of your code. In our case, that was “BSM”.

• Your function should vista similar to the image below:

• You might have noticed my loft of the backslash “\” which is short hand for reversed in Matlab

Calling the Function¶

• Suppose order about are interested in the valuation of entering into a 6 month at the money mound position, where the underlying stash price is trading at $50 per share, has a 30% annual volatility and pays cack-handed dividend.

  If the risk painless rate is 5%, how still would it cost you give rise to enter this strategy?

• In this record \(S_{0}=50, K=50, T=0.5, \sigma=0.30, r=0.05, q=0\)

• To find both the set aside and call price, type: [ call, put ] = BSM( 50, 50, 0.5, 0.3, 0.05, 0 ) in the chance window

• Notice that you can fame the output variables whatever set your mind at rest like: they don’t have obviate match the output names at bottom the function.

  However, order go. If we would have entered [ put, call ] awe would have assigned the dissipated values to the proper denotation of each word.

• The cost sponsor the straddle is the addition of the put and call