# 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 Dec 2, 2019 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. Feb 6, 2020 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.

• Additionally he should also consider the correlations among the asset classes and model them accordingly Jun 11, 2019 at 19:13
• Absolutely. But that is a second step, as maths get more complicated Jun 11, 2019 at 20:38
• the question asks for historical simulation (real data), yet the answer resorts to Monte Carlo simulation (artificial data)? The assets under consideration are a stock, a bond and a call option. Would using a stochastic process to artificially generate (Monte Carlo simulation) just one of these assets be out of bounds for a question on historical simulation? the ellipses in the table suggest the op already has the historical data as a given (or has one assets' data to compute the other assets) and does not need to generate them artificially Dec 2, 2019 at 2:16