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    ...
  • $\begingroup$ 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 $\endgroup$ – develarist Dec 2 '19 at 2:22

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.

  • $\begingroup$ Additionally he should also consider the correlations among the asset classes and model them accordingly $\endgroup$ – Dhruv Mahajan Jun 11 '19 at 19:13
  • $\begingroup$ Absolutely. But that is a second step, as maths get more complicated $\endgroup$ – alexbougias Jun 11 '19 at 20:38
  • $\begingroup$ 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 $\endgroup$ – develarist Dec 2 '19 at 2:16

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