Implementation of the Contingent Claim Model

gistfile1.txt

def prob_default(ticker):
    """ DEFINING THE FUNCTION WE WANT TO OPTIMISE"""
    def fun(x):
        va=x[0]
        siga=x[1]
        d1=(np.log(va/X)+(r+0.5*siga**2)*T)/(siga*np.sqrt(T))
        d2=d1-siga*np.sqrt(T)
        return [va*norm.cdf(d1)-X*np.exp(-r*T)*norm.cdf(d2)-ve,va*norm.cdf(d1)*siga/ve-sige]
    """DATA SELECTION"""
    start_date='2018-01-01'
    end_date='2018-12-31'
    # get data for that ticker
    daily_=daily[(daily.ticker==ticker)&(daily.date>=start_date)&(daily.date<=end_date)]
    # if after selecting the period, we get an empty dataframe, we skip that ticker
    if daily_.shape[0]==0:
        print(ticker+" is empty")
        return False
    daily_=daily_.reset_index()
    daily_.marketcap=daily_.marketcap*1e6
    
    """CALCULATING EQUITY RETURNS"""
    for j in range(1,daily_.shape[0]):
        daily_.loc[j-1,'returns']=np.log(daily_.loc[j-1,'marketcap']/daily_.loc[j,'marketcap'])
        
    """CALCULATING THE VOLATILITY OF EQUITY: SIGE"""
    sige=np.std(daily_.returns)*np.sqrt(252)
    
    """SOLVE SIMULTANEOUS EQUATIONS for 2018 and 2017"""
    #2018
    # Initialising values
    T=1
    r=0.017
    ve=daily_.loc[0,'marketcap']
    X=df[df.ticker==ticker]['debtc'].values[0]+.5*df[df.ticker==ticker]['debtnc'].values[0]
    sol = optimize.root(fun, [X+ve, sige*ve/(ve+X)])
    va=sol.x[0]
    siga=sol.x[1]
    
    #2017
    T=1
    r=0.015
    ve=daily_.loc[daily_.shape[0]-1,'marketcap']
    X=df[df.ticker==ticker]['debtc'].values[0]+.5*df[df.ticker==ticker]['debtnc'].values[0]
    sol = optimize.root(fun, [X+ve, sige*ve/(ve+X)])
    va_1=sol.x[0]
    siga=sol.x[1]
    #this gives the annual return
    mu=max((va-va_1)/va_1,r)
    DDt=(np.log(va/X)+(mu-0.5*siga**2)*T)/siga*np.sqrt(T)
    return norm.cdf(-DDt)