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This is a problem commonly faced by investment banks and buy-side firms (such as hedge funds) that deal in lots of derivatives. There isn't much more one can do than employ a few rules of thumb, and those rules have not changed much over the decades. In this case, those tricks look something like the following: First, let's assume you have your stock $S$ ...


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Let us say we have a yearly interest rate of $r$ that compounds over $n$ periods. With annual compounding that means $n=1$, with semi-annual compounding that means $n=2$ and with daily compounding that means $n=365$. We can calculate the value of putting \$1 into the bank account at time zero and withdrawing it after $n$ periods at time $t$ as $$ \left(1+\...


4

EDIT: Apologies, one more edit, but an important one: Note, as kindly pointed out to me by an interested reader a short time ago: there is a potential issue with the simple model I proposed. Namely, as it stands the model implies that the illiquid asset$Y_t$ is not a martingale. But all is not lost; the model could potentially still be used if the illiquid ...


2

Hull used a single Brownian driver. He did add, a few pages down, equation (31.15) (in my 7th edition) with $p$ independent Brownian drivers: $$ \frac{dF_k(t)}{F_k(t)} = \sum_{i=m(t)}^k \frac{\delta_iF_i(t) \sum_{q=1}^p\zeta_{i,q}(t)\zeta_{k,q}(t)}{1+\delta_iF_i(t)} dt +\sum_{q=1}^p \zeta_{k,q}(t) dz_q $$ with $\zeta_{k,q}(t)$ the component of the ...


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tl;dr: informally: You cannot know the value of the difference of two random variables by knowing their sum. Consider the following set $A =\{ \omega \in \Omega | W_1(t)(\omega) - W_2(t)(\omega) \in [0,1] \}$ This set is of course in the Filtration generated by $W_1$ and $W_2$ since the addition of measurable functions is measurable. Is this set in the (...


1

The flexible forward contract is very much like an American option: at each exercise date, you have the choice to receive the payoff $(S-K)$ or not. The difference with a regular option is that you must choose a date. In effect, this is a classical optimal stochastic control problem and may be solved using exactly the same techniques as for an American (or a ...


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