Learn FSHARP-FINANCE with Real Code Examples

let compoundInterest principal rate periods =
    principal * ((1.0 + rate) ** periods)

let amount = compoundInterest 1000.0 0.05 10.0
printfn "Compound Interest Amount: %f" amount

Compute the compound interest for a given principal, rate, and number of periods.

open System
open MathNet.Numerics.Distributions

let blackScholesCall S K r sigma T =
    let d1 = (log(S/K) + (r + 0.5 * sigma*sigma) * T) / (sigma * sqrt T)
    let d2 = d1 - sigma * sqrt T
    S * Normal.CDF(0.0,1.0,d1) - K * exp(-r*T) * Normal.CDF(0.0,1.0,d2)

let callPrice = blackScholesCall 100.0 100.0 0.05 0.2 1.0
printfn "Call Option Price: %f" callPrice

Calculate the price of a European call option using the Black-Scholes formula in F#.

open System
open MathNet.Numerics.Distributions

let simulateStockPath S0 mu sigma T steps =
    let dt = T / float steps
    let rnd = Normal(0.0,1.0)
    let rec loop S n acc =
        if n > steps then List.rev acc
        else let Snext = S * exp((mu - 0.5 * sigma*sigma)*dt + sigma*sqrt(dt)*rnd.Sample())
        loop Snext (n+1) (Snext::acc)
    loop S0 1 [S0]

let path = simulateStockPath 100.0 0.05 0.2 1.0 10
printfn "%A" path

Simulate a simple geometric Brownian motion for stock price evolution.

let portfolioReturn weights returns =
    List.map2 (*) weights returns |> List.sum

let weights = [0.6; 0.4]
let returns = [0.02; 0.03]
let pReturn = portfolioReturn weights returns
printfn "Portfolio Return: %f" pReturn

Compute the weighted return of a portfolio from individual asset returns.

let covMatrix = [[0.0004;0.0002];[0.0002;0.0003]]
let weights = [0.6;0.4]
let portfolioVariance =
    List.mapi (fun i row -> List.mapi (fun j x -> x * weights.[i] * weights.[j]) row |> List.sum) covMatrix |> List.sum
printfn "Portfolio Variance: %f" portfolioVariance

Calculate portfolio variance given asset covariance matrix and weights.

let portfolioStdDev variance = sqrt variance
let stdDev = portfolioStdDev 0.00028
printfn "Portfolio Std Dev: %f" stdDev

Compute the standard deviation of a portfolio from variance.

let sharpeRatio expectedReturn riskFreeRate stdDev = (expectedReturn - riskFreeRate)/stdDev
let sr = sharpeRatio 0.025 0.01 0.0167
printfn "Sharpe Ratio: %f" sr

Compute the Sharpe ratio of a portfolio.

let simulateMultiplePaths S0 mu sigma T steps nPaths =
    [1..nPaths] |> List.map (fun _ -> simulateStockPath S0 mu sigma T steps)

let paths = simulateMultiplePaths 100.0 0.05 0.2 1.0 10 5
printfn "%A" paths

Simulate multiple correlated stock price paths using geometric Brownian motion.

let forwardPrice S r T = S * exp(r*T)
let F = forwardPrice 100.0 0.05 1.0
printfn "Forward Price: %f" F

Compute the forward price of an asset given spot price, risk-free rate, and time to maturity.

let discountCashFlows cashFlows r =
    List.mapi (fun i cf -> cf / ((1.0 + r) ** float (i+1))) cashFlows |> List.sum

let pv = discountCashFlows [100.0;100.0;100.0] 0.05
printfn "Present Value: %f" pv

Compute present value of future cash flows.