IntermediateOptions, Derivatives & FinancePython

Run this module

cd "Finance - FX Tools"
python "fx_tools.py"

FX (Foreign Exchange) Tools¶

Core analytics for foreign exchange markets: no-arbitrage pricing, option valuation, and cross-rate calculations.

Functions¶

Function	Description
`forward_rate(spot, r_d, r_f, T)`	CIP-implied forward exchange rate
`forward_points(spot, r_d, r_f, T)`	Forward-spot differential in pips
`cip_deviation(spot, forward, r_d, r_f, T)`	Covered Interest Parity basis (bps)
`cross_rate(s_ab, s_ac)`	Derive B/C rate from two pairs
`triangular_arbitrage_profit(s_ab, s_bc, s_ca)`	Detect/quantify triangular arb
`garman_kohlhagen(S, K, r_d, r_f, sigma, T, type)`	European FX option pricing

Key Concepts¶

Covered Interest Rate Parity (CIP)¶

F = S × exp((r_d - r_f) × T) In theory, no arbitrage → forward rate is fully determined by spot + rate differential. In practice, CIP deviations (the "FX basis") are a significant source of hedge fund alpha.

Forward Points¶

Market convention: quote forward as "pips" above/below spot. Forward points = (F - S) / pip_size. Positive when domestic rate > foreign rate.

Garman-Kohlhagen¶

Black-Scholes extension for FX options. Foreign rate acts as a continuous dividend yield. Delta is expressed in domestic currency terms.

Example¶

from fx_tools import forward_rate, garman_kohlhagen, cip_deviation

# USD/EUR spot = 1.10, US rate 5%, EU rate 2%
F = forward_rate(1.10, r_domestic=0.05, r_foreign=0.02, T=1.0)  # ~1.1332

# FX call option
call = garman_kohlhagen(S=1.10, K=1.10, r_d=0.05, r_f=0.02, sigma=0.10, T=0.25)

Pip Conventions¶

Pair	Pip size
EUR/USD, GBP/USD	0.0001
USD/JPY	0.01
Most others	0.0001

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