Historical option data for expired Options contracts

[pascaloberle]

Hi,

I am looking to reconstruct Expired Options pricing with the help of ib_insync library and Interactive Brokers available data..
Because IB provides OPTION_IMPLIED_VOLATILITY as an output for reqHistoricalData I was thinking proceeding this way:

• Have a function to infer Expired Options Contract Prices from Black-Scholes Model:

def black_scholes(stock_price,strike_price,vol,time,rate,right="Call"):
    d1 = (np.log(stock_price/strike_price) + (rate + 0.5* vol**2)*time)/(vol*np.sqrt(time))
    d2 = (np.log(stock_price/strike_price) + (rate - 0.5* vol**2)*time)/(vol*np.sqrt(time))
    nd1 = norm.cdf(d1)
    nd2 = norm.cdf(d2)
    n_d1 = norm.cdf(-1*d1)
    n_d2 = norm.cdf(-1*d2)
    if right.capitalize()[0] == "C":
        return round((stock_price*nd1) - (strike_price*np.exp(-1*rate*time)*nd2),2)
    else:
        return round((strike_price*np.exp(-1*rate*time)*n_d2) - (stock_price*n_d1),2)

• Using the contract on the underlying stock assuming I have a valid ib connection opened elsewhere in my code to retrieve the data

def get_stock_history(symbol,whattoshow_string):
            contract = Stock(symbol, 'SMART', 'USD')
            ib.reqMarketDataType(2)
            bars = ib.reqHistoricalData(
                    contract,
                    endDateTime='',
                    durationStr='2 Y',
                    barSizeSetting='1 Hour',
                    whatToShow=whattoshow_string,
                    useRTH=True,
                    formatDate=1)
            ib.sleep(5)
            df = util.df(bars)
            df['date'] = pd.to_datetime(df['date'] ).dt.date
            return df

• I also have a handy function to compute maturity in the BSM based on an hourly time decay:

def hourCount(DF, expiry):
      DF["maturity"] = ((dt.datetime.strptime(expiry, "%Y-%m-%d") - pd.to_datetime(DF.index))/pd.Timedelta(hours=1))/(365*24)

• I could then get the data as below assuming I have an expiration date and strike from elsewhere I wish to backtest:

strike = 148
expiration_date = '2022-12-02'
symbol = 'AAPL'
historicalData = get_stock_history(symbol,'ADJUSTED_LAST')
impVolData = get_stock_history(symbol,'OPTION_IMPLIED_VOLATILITY')


option_price_call = pd.DataFrame(columns=["open","high","low","close"])
option_price_put = pd.DataFrame(columns=["open","high","low","close"])
hourCount(historicalData, expiration_date)
hourCount(impVolData, expiration_date)
historicalData = historicalData [(historicalData["maturity"] > 0)]
impVolData = impVolData[(impVolData["maturity"] > 0)]
for column in ["open","high","low","close"]:
        option_price_call[column] = black_scholes(historicalData[column], strike, impVolData[column], historicalData["maturity"], 0.03,right="Call")
        option_price_put[column] = black_scholes(historicalData[column], strike, impVolData[column], historicalData["maturity"], 0.03,right="Put")

Would that be a good approach to reconstruct/backtest the Expired Options contract pricing or am I overlooking something here? and maybe a smarter way to achieve this operation?

Thanks in advance for your suggestions! (y)