# Historical Simulation of Bond, Stock and Option Portfolio

If I have a portfolio consisting of

1-one stock of unit price equal to S,

2-one 9% coupon American bond with 20 years to maturity and a par value of $1000, 3-and one European call option on the stock of unit price C who matures in 3 months and the strike price of the option \$200

How to calculate simulated portfolio value over the next N days, from these inputs:

    Date (t) St (\$) rt (required yield) σt (volatility) int. (three month rate)
Day 1    201    12 %                23 %            0.9 %
Day 2    203    12.3 %              20 %            0.6 %
...
Day N    ...

• the question is on historical simulation. would that count as backtesting given that the object is a portfolio? These two terms are often mistaken for one another – develarist Dec 2 '19 at 2:22
• What is your objective here? Absent historical data, your portfolio results will comprise a model for the equity portion, a second for the debt and a third for their correlations, all with their own assumptions. Calculating portfolio value of the portfolio of these is so filled with assumptions as to be pretty close to useless for anything in the real world excluding maybe pricing of some structured product. – Chris Feb 6 '20 at 21:54

You can assume a stochastic process for each security, and conduct a Monte Carlo simulation, generating different realization of porfolio values. For the stock, a Geometric Browinian Motion or a broader Levy process, would be ok. This should be the process of the underlying stock in case of the option, in order to price the option. For the bond, define a stochastic process for the interest rates (e g Ohrstein-Uhlenbeck), and through the present value of Coupons and Principal, calculate the bond price. That should give you a distribution of future portfolio values ($$V_{t+2}$$), or equivalently the return distribution of the portfolio.