added montecarlo blacksholes pricer

Author: aleCombi

src/Hedgehog2.jl

@@ -11,6 +11,8 @@ include("market_inputs/market_inputs.jl")
 include("pricing_methods/pricing_methods.jl")
 include("pricing_methods/black_scholes.jl")
 include("pricing_methods/cox_ross_rubinstein.jl")
+include("pricing_methods/montecarlo.jl")
+
 include("sensitivity_methods/delta_methods.jl")
 include("stochastic_processes/stochastic_processes.jl")
 

src/pricing_methods/black_scholes.jl

@@ -1,5 +1,14 @@
 # Black-Scholes pricing function for European vanilla options
 
+export BlackScholesMethod
+
+"""
+The Black-Scholes pricing method.
+
+This struct represents the Black-Scholes pricing model for option pricing, which assumes a lognormal distribution for the underlying asset and continuous hedging.
+"""
+struct BlackScholesMethod <: AbstractPricingMethod end
+
 """
 Computes the price of a vanilla European call or put option using the Black-Scholes model.
 

src/pricing_methods/cox_ross_rubinstein.jl

@@ -1,5 +1,7 @@
 # Cox-Ross-Rubinstein Binomial Tree Pricing Implementation
 
+export CoxRossRubinsteinMethod
+
 """
 The Cox-Ross-Rubinstein binomial tree pricing method.
 

src/pricing_methods/montecarlo.jl

@@ -0,0 +1,18 @@
+# a montecarlo method is defined by an SDEProblem or a NoiseProblem.
+# the SDE problem needs market data and a payoff to be defined
+abstract type MontecarloMethod <: AbstractPricingMethod end
+
+struct BSMontecarlo <: MontecarloMethod
+    trajectories
+end
+
+# we could make an ExactMontecarlo, dispath to get the noise problem and always make just one step.
+function compute_price(payoff::VanillaOption{European, C, Spot}, market_inputs::BlackScholesInputs, method::BSMontecarlo) where {C}
+    T = Dates.value.(payoff.expiry .- marketInputs.referenceDate) ./ 365  # Assuming 365-day convention
+    noise = GeometricBrownianMotionProcess(market_inputs.r, market_inputs.sigma, market_inputs.referenceDate, 0)
+    problem = NoiseProblem(noise, (0, T))
+    ensemble_problem = EnsembleProblem(problem)
+    solution = solve(ensemble_problem; dt=T, trajectories = method.trajectories) # its an exact simulation, hence we use just one step
+    mean_payoff = mean(payoff.(last.(solution.u)))
+    return mean_payoff
+end

src/pricing_methods/pricing_methods.jl

@@ -1,5 +1,5 @@
 # Exported Types and Functions
-export AbstractPricingMethod, BlackScholesMethod, Pricer, compute_price, CoxRossRubinsteinMethod
+export AbstractPricingMethod, Pricer, compute_price
 
 """
 An abstract type representing a pricing method.
@@ -8,13 +8,6 @@ All pricing methods, such as Black-Scholes or binomial trees, should inherit fro
 """
 abstract type AbstractPricingMethod end
 
-"""
-The Black-Scholes pricing method.
-
-This struct represents the Black-Scholes pricing model for option pricing, which assumes a lognormal distribution for the underlying asset and continuous hedging.
-"""
-struct BlackScholesMethod <: AbstractPricingMethod end
-
 """
 A pricer that calculates the price of a derivative using a given payoff, market data, and a pricing model.