Py-based onestage tree model valuation of call & put options

from math import exp, sqrt

def replicate(stockPrice, strikePrice, optionType, optionMaturity, stockVolatility, interestRate):
    # Valuate an option by making a replicating portfolio of a certain option.
    # Stock price is the current stock price.
    # Strike price is the strike price of the option.
    # Option type determines whether it is a call or put option.
    # Option maturity gives us the period in which the option matures.
    # Stock volatility gives us the standard deviation of the stock.
    # Interest rate is the used rate of return on the stock lend.

    # Determine the up and down side changes in a certain maturity period.
    upsideChange    = exp(stockVolatility * sqrt(optionMaturity))
    downsideChange  = 1/upsideChange

    # Determine the corresponding stock prices.
    upsidePrice     = stockPrice * upsideChange
    downsidePrice   = stockPrice * downsideChange

    # Set up the payoff scheme.
    payoffLeft      = 0
    payoffRight     = 0

    if downsidePrice <= strikePrice:
        payoffLeft = 0
    else:
        payoffLeft = downsidePrice - strikePrice

    if upsidePrice <= strikePrice:
        payoffRight = 0
    else:
        payoffRight = upsidePrice - strikePrice

    # Calculate the option delta
    if optionType == "call":
        optionDelta = (payoffRight - payoffLeft) / (upsidePrice - downsidePrice)
    else:
        optionDelta = (payoffLeft - payoffRight) / (upsidePrice - downsidePrice)

    # Replicate the payoffs by determining the buy/sell of shares and borrow/lend of money.
    if optionType == "call":
        buySharePrice   = optionDelta * downsidePrice
        borrowPrice     = buySharePrice / ((1 + interestRate) ** optionMaturity)
    else:
        sellSharePrice  = optionDelta * upsidePrice
        lendPrice       = sellSharePrice / ((1 + interestRate) ** optionMaturity)

    # Calculate the value of the option
    if optionType == "call":
        optionValue = (optionDelta * stockPrice) - borrowPrice
    else:
        optionValue = (optionDelta * stockPrice) + lendPrice

    return optionValue