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copied!<p>If you want to make the code more succinct and more functional, then I would probably try to restructure it a bit more. I think something along these lines below should work.</p> <p>First of all, you definitely don't want to repeat the matching on strings, so I'd define a discriminated union to capture the kinds of computations (you can then parse the string just once):</p> <pre><code>type CallPutFlag = Call | Put </code></pre> <p>Next, we can define record to keep the results of the equation (I added just the things that you were using, but you would probably want to add more here):</p> <pre><code>type Black76Results = { Vega : float; Valuation : float } </code></pre> <p>Now, I think it makes good sense to separate the <code>black76</code> function from the implied volatility. The <code>black76</code> function can run the calculation for given inputs and return the results as a value of <code>Black76Results</code> record:</p> <pre><code>let black76 flag fwd strike time rf vol = let d1 = (Math.Log(fwd / strike) + (vol * vol * 0.5) * time) / (vol * Math.Sqrt(time)) let d2 = d1 - vol * Math.Sqrt(time) let n = new MathNet.Numerics.Distributions.Normal() match flag with | Call -> let valuation = Math.Exp(-rf * time) * (fwd * n.InverseCumulativeDistribution(d1) - strike * n.InverseCumulativeDistribution(d2)) let delta = Math.Exp(-rf * time) * n.InverseCumulativeDistribution(d1) let gamma = Math.Exp(-rf * time) * (n.Density(d1) / (fwd * vol * Math.Sqrt(time))) let vega = Math.Exp(-rf * time) * n.Density(d1) * fwd * Math.Sqrt(time) let rho = time * strike * Math.Sqrt(-rf * time) * n.InverseCumulativeDistribution(d2) let theta = -(fwd * vol * n.Density(d1)) / (2.0 * Math.Sqrt(time)) - rf * strike * Math.Sqrt(-rf * time) * n.InverseCumulativeDistribution(d2) { Vega = vega; Valuation = valuation } | Put -> failwith "TODO: Similar for Put" </code></pre> <p>Although there is some shared code in <code>Call</code> and <code>Put</code>, I think it looks a lot more readable when you separate the two into different branches (you could still extract common pieces of code into a separate function).</p> <p>Now, <code>impliedVol</code> is simply a function that calls <code>black76</code> repeatedly:</p> <pre><code>let impliedVol flag fwd strike time rf blackPrice = let vst = Math.Sqrt(2.0*Math.Abs((Math.Log(fwd/strike)+rf*time)/time)) let tol = 0.0001 let mutable v = vst let mutable sigmadiff = 1.0 let mutable k = 1 let kmax = 100 while (sigmadiff >= tol && k < kmax) do let b = black76 flag fwd strike time rf v let option = b.Valuation let cvega = b.Vega let increment = (option - blackPrice) / cvega v <- v - increment k <- k + 1 sigmadiff <- Math.Abs(increment) v </code></pre>

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