Adjusting inputs form bs, scaling corrected in carr madan

Author: aleCombi

examples/binomial_tree_vega.jl

@@ -9,9 +9,10 @@ american_payoff = VanillaOption(strike, expiry, Hedgehog2.American(), call_put,
 # define market inputs
 reference_date = Date(2017, 6, 29)
 rate = 0.013047467783283154
-forward = 5.6525
+T = Dates.values(expiry - reference_date) / 365
+spot = 5.6525 * exp(-rate*T)
 sigma = 0.1689900715
-market_inputs = BlackScholesInputs(reference_date, rate, forward, sigma)
+market_inputs = BlackScholesInputs(reference_date, rate, spot, sigma)
 
 # create Cox Ross Rubinstein pricer
 steps = 800

examples/binomial_tree_vega_pluto.jl

@@ -40,10 +40,11 @@ american_payoff = VanillaOption(strike, expiry, Hedgehog2.American(), call_put,
 
 # define market inputs
 reference_date = Date(2017, 6, 29)
+T = Dates.values(expiry - reference_date) / 365
 rate = 0.013047467783283154
-forward = 5.6525
+spot = 5.6525 * exp(r*T)
 sigma = 0.1689900715
-market_inputs = BlackScholesInputs(reference_date, rate, forward, sigma)
+market_inputs = BlackScholesInputs(reference_date, rate, spot, sigma)
 
 # create Cox Ross Rubinstein pricer
 steps = 800

examples/black_vs_binomial_tree.jl

@@ -11,9 +11,9 @@ euro_payoff = VanillaOption(strike, expiry, Hedgehog2.European(), call_put, unde
 # define market inputs
 reference_date = Date(2020, 1, 1)
 rate = 0.2
-forward = 1
+spot = 1
 sigma = 0.4
-market_inputs = BlackScholesInputs(reference_date, rate, forward, sigma)
+market_inputs = BlackScholesInputs(reference_date, rate, spot, sigma)
 
 # create analytical black scholes pricer
 bs_method = BlackScholesMethod()

examples/carr_madan.jl

@@ -5,14 +5,13 @@ using Revise, Hedgehog2, BenchmarkTools, Dates
 # Define market inputs
 reference_date = Date(2020, 1, 1)
 rate=0.2
-spot=1
+spot=100
 sigma=0.4
 market_inputs = BlackScholesInputs(reference_date, rate, spot, sigma)
-market_inputs_bs = BlackScholesInputs(reference_date, rate, exp(rate)*spot, sigma)
 
 # Define payoff
 expiry = reference_date + Day(365)
-strike = 1.5
+strike = 150
 payoff = VanillaOption(strike, expiry, Hedgehog2.European(), Hedgehog2.Call(), Hedgehog2.Spot())
 
 # Define carr madan method
@@ -24,7 +23,7 @@ method = Hedgehog2.CarrMadan(α, boundary)
 carr_madan_pricer = Pricer(payoff, market_inputs, method)
 
 # Define analytical pricer
-analytical_pricer = Pricer(payoff, market_inputs_bs, BlackScholesMethod())
+analytical_pricer = Pricer(payoff, market_inputs, BlackScholesMethod())
 
 println(analytical_pricer())
 println(carr_madan_pricer())

examples/carr_madan_heston.jl

@@ -15,7 +15,7 @@ V0 = 0.010201    # Initial variance
 r = 0.0319      # Risk-free rate
 T = 1.0       # Time to maturity
 market_inputs = Hedgehog2.HestonInputs(reference_date, r, S0, V0, κ, θ, σ, ρ, r)
-bs_market_inputs = BlackScholesInputs(reference_date, r, S0, sqrt(V0))
+bs_market_inputs = BlackScholesInputs(reference_date, r, exp(rate)*S0, sqrt(V0))
 # Define payoff
 expiry = reference_date + Day(365)
 strike = 100

src/market_inputs/market_inputs.jl

@@ -16,13 +16,13 @@ It is assumed that the volatility is annual.
 struct BlackScholesInputs <: AbstractMarketInputs
     referenceDate
     rate
-    forward
+    spot
     sigma
 end
 
 function log_distribution(m::BlackScholesInputs)
-    r, σ = m.rate, m.sigma
-    d(t) = Normal((r - σ^2 / 2)t, σ√t)  
+    r, σ, S0 = m.rate, m.sigma, m.spot
+    d(t) = Normal(log(S0) + (r - σ^2 / 2)t, σ√t)  
     return d
 end
 

src/pricing_methods/black_scholes.jl

@@ -46,12 +46,12 @@ where:
 - The function supports both call and put options through the `cp` factor, ensuring a unified formula.
 """
 function compute_price(payoff::VanillaOption{European, A, B}, marketInputs::BlackScholesInputs, ::BlackScholesMethod) where {A,B}
-    F = marketInputs.forward
     K = payoff.strike
     r = marketInputs.rate
     σ = marketInputs.sigma
     cp = payoff.call_put()
     T = Dates.value.(payoff.expiry .- marketInputs.referenceDate) ./ 365  # Assuming 365-day convention
+    F = marketInputs.spot*exp(r*T)
     d1 = (log(F / K) + 0.5 * σ^2 * T) / (σ * sqrt(T))
     d2 = d1 - σ * sqrt(T)
     return exp(-r*T) * cp * (F * cdf(Normal(), cp * d1) - K * cdf(Normal(), cp * d2))

src/pricing_methods/carr_madan.jl

@@ -7,7 +7,7 @@ struct CarrMadan <: AbstractPricingMethod
 end
 
 # in distribution.jl t is Real, hence we need to redefine it.
-cf(d::Normal, t) = exp(im * t * d.μ- d.σ^2 / 2 * t^2)
+cf(d::Normal, t) = exp(im * t * d.μ - d.σ^2 / 2 * t^2)
 
 function compute_price(payoff::VanillaOption{European, Call, Spot}, market_inputs::I, method::CarrMadan) where I <: AbstractMarketInputs
     damp = exp(- method.α * log(payoff.strike)) / 2π

src/pricing_methods/cox_ross_rubinstein.jl

@@ -108,9 +108,11 @@ Computes the price of a vanilla option using the Cox-Ross-Rubinstein binomial tr
 """
 function compute_price(payoff, market_inputs, method::CoxRossRubinsteinMethod)
     steps = method.steps
-    ΔT = Dates.value.(payoff.expiry - market_inputs.referenceDate) / 365 / steps  # Assuming ACT/365 day count
+    T = Dates.value.(payoff.expiry - market_inputs.referenceDate) / 365
+    forward = market_inputs.spot * exp(market_inputs.rate * T)
+    ΔT = T / steps  # Assuming ACT/365 day count
     u = exp(market_inputs.sigma * sqrt(ΔT))  # Up-move factor
-    forward_at_i(i) = market_inputs.forward * u .^ (-i:2:i)
+    forward_at_i(i) = forward * u .^ (-i:2:i)
     underlying_at_i(i) = binomial_tree_underlying(i, forward_at_i(i), market_inputs.rate, ΔT, payoff.underlying)
 
     # Up probability in forward measure