Pricing of options and other financial products
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Latest commit 352759b Dec 14, 2016 jan fajfr fixing the dep to 3.8 on math numerics


Nuget Package Build status

Small library that can be used to price options (Black Scholes and Binomial pricing), generate payoff charts and maybe analyze stock prices. It was based by Tomas Petricek's Financial Computing in F# series. I have added binomial pricing, different algorithm to estimate the volatility and few other features.

The Pricer.Core project does not depend on anything else than BCL, so it can be transpiled into JavaScript using Fable. A sample application Pricer.Fabled is part of the solution and compiled is available here:

Options pricing

The library contains a model for describing options and stocks. Besides the options description one needs the stock's volatility, current price and interest free rate.

let stock = {
  CurrentPrice = 201.0
  Volatility = 0.124
  Rate = 0.03

let option = {
    Strike = 250.0
    Expiry = DateTime.Now.AddDays(90.)
    Direction = 1.0
    Kind = Call
    Style = American
    PurchaseDate = DateTime.Now

let price = Options.blackScholes stock option
let binomialPrice = Options.binomial stock option 2000

Binomial pricing takes also the depth of the binomial tree as parameter, the result is Pricing record which contains the Premium and Delta.

Alternatively you can obtain the historical volatility and current price from small referential data module which uses free Quandl API. The bellow example uses trading data for last 60 days. The library uses free data from Quandl to estimate the volatility for stocks. The rate for now is fixed.

let stock = Stocks.stockInfo LSE "VOD" (Some (DateTime.Now.AddDays -60.0)) (Some DateTime.Now)

Payoff charts data generation

You can generate payoff charts data for any strategy. Strategy is composed of legs which can be already priced. The library also contains method to generate example strategies that just accept the Stock as parameter. Here is how to visualize the result of priced strategy.

let strategy = StrategiesExamples.callSpread stock
let strategyData,legsData = Options.getStrategyData strategy
let strategyLine = Chart.Line(strategyData,Name = strategy.Name) |> Chart.WithSeries.Style(Color = Color.Red, BorderWidth = 5)
let legsLines = legsData |> Seq.mapi (fun i (leg,legData) -> Chart.Line(legData,leg.Definition.Name))
let allLines = legsLines |> Seq.append [strategyLine]
let chart = Chart.Combine allLines |> Chart.WithLegend(true)

Stock price and volatility

You can also use the library only to get the stock data and perform some basics analysis, like for instance floating averages:

let ticker,data = MarketData.stock LSE "VOD" (Some (DateTime.Now.AddDays -60.0)) (Some DateTime.Now)
let tenDaysAvg = Stocks.floatingAvg 10 data
let fiveDaysAvg = Stocks.floatingAvg 5 data
Chart.Combine [
    Chart.Line((data|>Seq.sortBy Stocks.tradingDay |> (fun tick -> tick.Date, tick.Close)),Name = "Day")
    Chart.Line(tenDaysAvg,Name="10 days avg")
    Chart.Line(fiveDaysAvg,Name="5 days avg")
] |> Chart.WithLegend true

There are several ways of estimating the historical volatility of the stock. The standard and simplest method is Close To Close estimation when log returns based on closing prices are compared. There is also a second mode for pricing volatility which uses opening prices, both described in this blog

let ticker,data = MarketData.stock EURONEXT "ATI" (Some (DateTime.Now.AddDays -180.0)) (Some DateTime.Now)
let vol = Stocks.estimateVol CloseVsClose data
let vol2 = Stocks.estimateVol CloseVsOpen data

Building & Contributing

Pricer uses FAKE as it's build system. Fake is included in the repository and a proxy fake.cmd script runs any of fake tasks and passes the parameters.

fake Test

Pricer.Fabled is transpiled into JavaScript, but depends on Pricer.Core which has to be transpiled first. A build.cmd command is available in the Pricer.Fabled folder to chain both fable commands.