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6

You are using Put vs Call I think. You can convert the put price to call using put call parity: 3+5.55 when you assume zero interest rate. This would be more important for the other approximations. The main problem with the approximation formula is that, as noted in the comments in the answer you referenced, your approximation will not be accurate for non-...


3

@Gordon has already given the answer but here is a little more notes to it... At time time $T_2$ the holder receives $X=(S_{T_1}-K)^+$. According to Risk Neutral Valuation the value at time $t$ $(t<T_1<T_2)$ is $$V_t = e^{-r(T_2-t)}E_t[(S_{T_1}-K)^+] = \\ e^{-r(T_2-t+T_1-T_1)}E_t[(S_{T_1}-K)^+]=\\ e^{-r(T_2-T_1)}e^{-r(T_1-t)}E_t[(S_{T_1}-K)^+] $$ $e^...


2

At $t_1$, this payoff can be priced using the Margrabe formula as used for pricing an exchange option. See Margrabe Formula here Using the notations in the question and those used the hyperlinked document above - $Price_{t_1} = P_{t_1}e^{(\mu_P-r)\tau}\Phi(d_+) -HR \times G_{t_1}e^{(\mu_G-r)\tau}\Phi(d_-) \tag{1}$ $Price_0$ is the discounted value of $...


1

As Alex C says in the comments, Longstaff and Schwarz did consider multiple factors and mention it as one of the advantages (page 114 in the journal): By its nature, simulation is a promising alternative to traditional finite difference and binomial techniques and has many advantages as a framework for valuing, risk managing, and optimally exercising ...


1

Here's my $1/50. Please be free to raise any suggestions. Don't regress the split cashflows respectively as in TF, just regress the whole continuation value instead. When the bond is in the callable period, we'll have to use all paths; Otherwise, when in the convertible period, only consider the paths where conversion value > straight bond value (or should ...


1

If you imply real assets as the "left" side of the balance sheet, then there are recent papers which examine simultaneously both the option to invest (growth options), issuance of debt/equity and the ability to determine endogenously the default barrier. Although, their complexity may require numerical solutions and increased mathematical complexity that ...


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