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taumuon/Option Pricing Explicit Finite Difference F#

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Revisions

  1. taumuon revised this gist Feb 20, 2013. 1 changed file with 2 additions and 2 deletions.
    4 changes: 2 additions & 2 deletions Option Pricing Explicit Finite Difference F#
    View file
    Original file line number Diff line number Diff line change
    @@ -18,13 +18,13 @@ let calcTimeStep vol numberAssetSteps expiration =
    (dT, numberTimeSteps)

    let optionValue vol intRate payoff strike expiration numberAssetSteps =
    let payoffCurried = payoff strike
    let payoffForStrike = payoff strike // partially apply
    let dS = calcAssetStep strike numberAssetSteps
    let timeStep = calcTimeStep vol numberAssetSteps expiration
    let dT = fst timeStep
    let numberTimeSteps = snd timeStep
    let S = [|for i in 0 .. numberAssetSteps -> float i * dS|]
    let initialValues = [|for i in 0 .. numberAssetSteps -> payoffCurried S.[i]|]
    let initialValues = [|for i in 0 .. numberAssetSteps -> payoffForStrike S.[i]|]

    let calc (prev, curr, next) S =
    let delta = (next - prev) / 2.0 / dS; // central difference
  2. taumuon revised this gist Feb 20, 2013. 1 changed file with 2 additions and 2 deletions.
    4 changes: 2 additions & 2 deletions Option Pricing Explicit Finite Difference F#
    View file
    Original file line number Diff line number Diff line change
    @@ -18,13 +18,13 @@ let calcTimeStep vol numberAssetSteps expiration =
    (dT, numberTimeSteps)

    let optionValue vol intRate payoff strike expiration numberAssetSteps =
    let callPayoffCurried = payoff strike
    let payoffCurried = payoff strike
    let dS = calcAssetStep strike numberAssetSteps
    let timeStep = calcTimeStep vol numberAssetSteps expiration
    let dT = fst timeStep
    let numberTimeSteps = snd timeStep
    let S = [|for i in 0 .. numberAssetSteps -> float i * dS|]
    let initialValues = [|for i in 0 .. numberAssetSteps -> callPayoffCurried S.[i]|]
    let initialValues = [|for i in 0 .. numberAssetSteps -> payoffCurried S.[i]|]

    let calc (prev, curr, next) S =
    let delta = (next - prev) / 2.0 / dS; // central difference
  3. taumuon created this gist Feb 20, 2013.
    88 changes: 88 additions & 0 deletions Option Pricing Explicit Finite Difference F#
    View file
    Original file line number Diff line number Diff line change
    @@ -0,0 +1,88 @@
    open System

    let callPayoff strike spot = max (spot - strike) 0.0
    let putPayoff strike spot = max (strike - spot) 0.0

    let triplewise (source: seq<_>) =
    source
    |> Seq.windowed 3
    |> Seq.map (fun triple -> (triple.[0], triple.[1], triple.[2]))

    let calcAssetStep strike numberAssetSteps =
    2.0 * strike / float numberAssetSteps // 'infinity' is twice the strike

    let calcTimeStep vol numberAssetSteps expiration =
    let timeStep = 0.9 / (vol * vol) / float (numberAssetSteps * numberAssetSteps) // For stability
    let numberTimeSteps = (int (expiration / timeStep)) + 1
    let dT = (expiration / float numberTimeSteps) // ensure expiration is an integer number of time steps away
    (dT, numberTimeSteps)

    let optionValue vol intRate payoff strike expiration numberAssetSteps =
    let callPayoffCurried = payoff strike
    let dS = calcAssetStep strike numberAssetSteps
    let timeStep = calcTimeStep vol numberAssetSteps expiration
    let dT = fst timeStep
    let numberTimeSteps = snd timeStep
    let S = [|for i in 0 .. numberAssetSteps -> float i * dS|]
    let initialValues = [|for i in 0 .. numberAssetSteps -> callPayoffCurried S.[i]|]

    let calc (prev, curr, next) S =
    let delta = (next - prev) / 2.0 / dS; // central difference
    let gamma = (next - 2.0 * curr + prev) / dS / dS // central difference
    let theta = -0.5 * vol * vol * S * S * gamma - intRate * S * delta + intRate * curr // Black-Scholes
    curr - float dT * theta

    let calc (k, prevValues:float[]) =
    if k = (numberTimeSteps + 1) then
    None
    else
    let values = prevValues
    |> Seq.ofArray
    |> triplewise
    |> Seq.mapi (fun idx vals -> calc vals S.[idx + 1])
    let b0 = prevValues.[0] * (1.0 - intRate * float dT) // boundary condition at S=0
    let placeHolder = 0.0
    let valuesSeq = seq {
    yield b0
    yield! values
    yield placeHolder }
    let valuesArray = Seq.toArray valuesSeq
    let b1 = 2.0 * valuesArray.[numberAssetSteps - 1] - valuesArray.[numberAssetSteps - 2] // boundary condition at S=infinity
    valuesArray.[valuesArray.Length - 1] <- b1
    Some(valuesArray, (k+1, valuesArray))

    seq
    { yield initialValues
    yield! Seq.unfold calc (1, initialValues) }

    // use gnuplot with the following:
    // set zrange [0:120]
    // set xlabel "Time"
    // set ylabel "Asset"
    // set zlabel "Option value"
    // splot "out.dat"
    let outputVals (filename:string) (dS:float) (dT:float) (vals:seq<float[]>) =
    use textWriter = new System.IO.StreamWriter(filename)
    vals |> Seq.iteri (fun i s ->
    for j = 0 to (s.Length - 1) do
    textWriter.WriteLine("{0} {1} {2}", dT * float i, dS * float j, s.[j]))

    [<EntryPoint>]
    [<STAThread>]
    let main argv =
    let vol = 0.2
    let interestRate = 0.05
    let strike = 100.0
    let expiry = 1.0
    let numberAssetSteps = 20
    let vCall = optionValue vol interestRate callPayoff strike expiry numberAssetSteps

    let dS = calcAssetStep strike numberAssetSteps
    let timeStep = calcTimeStep vol numberAssetSteps expiry
    let dT = fst timeStep

    vCall |> outputVals "E:\\temp\\Call.dat" dS dT

    let vPut = optionValue vol interestRate putPayoff strike expiry numberAssetSteps
    vPut |> outputVals "E:\\temp\\Put.dat" dS dT
    0 // return an integer exit code