Questions tagged [proof]

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Martingale positive price process

I hope you can help me with this problem. In my lecture notes, my professor stated that for a state price deflator $\phi\in L_{n+1}^2(P, F)$ (F being a filtration) and a strictly positive price ...
Wombat's user avatar
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Filipovic: Where is it used that the world is deterministic

In this text (Damir Filipovic, Term-Structure Models, Springer, 2009) $P(t,T)$ denotes the price of a zero-coupon bond at time $t$ with maturity $T$. I cannot see where the proof uses the ...
Landscape's user avatar
  • 548
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Black-Litterman proof with P=I and Omega=tau*Sigma

Elsewhere on this site (link), Richard notes that \begin{equation} \Pi_{BL} = \frac{1}{2} \Pi + \frac{1}{2}Q, \end{equation} so long as we set $ P = I $ (where $I$ is the identity matrix) and $\Omega ...
user221772's user avatar
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HJM Model proofs

I am looking for a source that possibly has the proofs for the material in the first paper on the HJM model Heath, David, et al. “Bond Pricing and the Term Structure of Interest Rates: A New ...
Heisenberg's user avatar
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How to derive the Greek theta from Black-Scholes solution formula?

Which are the steps to compute the theta greek from the BS solution: $$c(t, x) = xN(d_+(T-t,x)) - K e ^{-r(T-t)}N(d_-(T-t,x))$$ with: $$ d_\pm (T-t, x) = \dfrac{1}{\sigma \sqrt{T-t}} \left[ \ln \...
Archimede's user avatar
  • 111
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No arbitrage argument for the price process of a forward contract

I was reading the book Stochastic Calculus for Finance II by Shreve and I read the proof that the forward price for the underlying $S$ at time $t$ with maturity $T$ is given by $$ For_S(t,T) = \frac{S(...
julian2000P's user avatar
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Price of financial assets at $t=0$ in Black-Scholes framework

Given the share price equation $$ dS_t=rS_tdt+\sigma S_tdW_t $$ working in the framework of Black-Scholes model, find the price at $t=0$ of the following two financial assets: (a) The asset pays at $t=...
Tyrell's user avatar
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Understanding arbitrage, defined as a series of cash flows

I'm currently catching up on material presented in the edX-MIT course Foundations of Mondern Finance 1, in which they present a definition of arbitrage that doesn't quite make sense to me. Informally, ...
Michael Wheeler's user avatar
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Can we proof the boundary condition for the Black Scholes derived from a replicating Portfolio?

So for Black Scholes we know that the PDE is the follwing: ${\frac {\partial V}{\partial t}}+{\frac {1}{2}}\sigma ^{2}S^{2}{\frac {\partial ^{2}V}{\partial S^{2}}}=rV-rS{\frac {\partial V}{\partial S}}...
Nikolai Kl's user avatar
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CVA formula proof

I'm struggling to prove the CVA formula in this paper. Equation (3) is the result of computing the expectation of formula (1). Could you please show me how to prove that?
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