I'm trying to build a Monte Carlo for a convertible and was hoping to get some tips on basic questions. Assume the conversion price is $10 and convertible anytime by the holder, par value and liq pref is $1000 (so initially converts into 100 shares), maturity in 5 years, underlying is $8/share. Also, if the underlying is at least $15 for 20 out of 30 consecutive trading days, the company can force redemption. Also assume risk-free rate of 5% and credit spread of 6% (so 11% required yield on the security).1. If I were to run a Monte Carlo on the stock price and get to year 5, what discount rate do I use for that payoff? On one hand, if the holder does not convert, I would have discounted the $1000 by the 11% rate. However, what if the converted value were $990? I would discount that by the risk-free rate. But the holder wouldn't convert to get $990 when he could have taken $1000. It seems wrong to use the risk-free rate when discounting back a "bond component" when the bond has an 11% required rate of return.2. An alternative I thought was to simulate not the underlying price, but the stock + value of the convert and then parcel out cash flows to the convert (e.g., if the total value of the underlying was $100 million and the convert was worth $10 million, I would run a Monte Carlo on a $110 million and take the returns to the convert from that). However, how do I test the "20 out of 30 days" condition? What that seems to need is that every point in the simulation, I would need to value the convert to determine the remaining equity value, which then gets converted to a per share value; this seems computationally expensive and difficult to do.Thanks for any advice you can provide!

QuoteOriginally posted by: tttchen1. If I were to run a Monte Carlo on the stock price and get to year 5, what discount rate do I use for that payoff?wouldn't the interest rate be stochastic also ?

QuoteOriginally posted by: ppauperQuoteOriginally posted by: tttchen1. If I were to run a Monte Carlo on the stock price and get to year 5, what discount rate do I use for that payoff?wouldn't the interest rate be stochastic also ?I agree with ppauper; the bond V = V(S, r, t) and then you have two SDEs to simulate I reckon:dS = mu*dt + vol * dW1dr = u * dt + w * dW2and S, r are correlatedThen apply MC.