# Questions tagged [proof]

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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 ...
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### Survival probabilities starting from CDS spreads

How is that possible to get survival probabilities starting from CDS spread? Could you please provide me with a demonstration? What is more, is that true that CDS Zero type is necessary so as to get ...
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### Relationship between Vega and Gamma in Black-Scholes model

my question is the following one: I don't manage to prove that, in Black-Scholes model, single-signed Gamma options have values that are monotonic in the volatility. I am looking for an exhaustive and ...
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### Proof: Brownian Motion Path Continious with Probability One [closed]

How can one show that the paths of the standard Wiener process are continuous in $T$ with probability one? Can we just proof it with the assumption of independence ? Thank You in advance!
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### Proving Scaled Random Walk Approaches Normal Distribution

I'm reading Stochastic Calculus for Finance II: Continuous-Time Models by Steven Shreve and I don't understand how he went from the equation on the left to the middle one. If it helps, this section is ...
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### Expected Shortfall monotonicity

I have to show monotonicity for a more general case than the expected shortfall. I have to show that $E(X|X \geq a) \geq E(X|X \geq b), \forall a,b \in \mathbb{R}$ so that $a\geq b$ and $F_X(a-)<1$....
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### Can someone prove (or disprove) this assertion about the normal distribution? [closed]

Let $X$ be distributed as a $Normal (\mu, \sigma^2)$. Then for a fixed $\mu$ it is always the case that: \frac{90th quantile-10th quantile}{\sigma}=constant \quad \forall \sigma>0 ...
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### Showing BM $W(s)$ is independent of $W(t)-W(s)$ [closed]

Consider $0\leq s<t$ where $t,s$ represent time index. I want to show a Brownian motion $W(s)$ is independent of $W(t)-W(s)$. Specifically, show that $E[W(s)(W(t)-W(s))]=0$ Proof: Writing $W(s)$...
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### Proof that adding some quantity of stocks in a portfolio of option does not change the portfolio Gamma

I would like to proof mathematically and intuitively that adding some quantity of underlying to a portfolio of option does not change the overall gamma. Can you help me?
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### Ito isometry and the covariance of an Ito process

Let $(B_t)_{t \geq 0}$ et $(W_t)_{t \geq 0}$ be two independent Brownian motions and let $f: \mathbb{R} \rightarrow \mathbb{R}$ a deterministic function of time. We define the following process: \...
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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 ...
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### Spot-Forward Relationship - Proof

Does anyone know of a decent proof for the spot-forward relationship of a currency? I've been looking on Google for hours and I'm not getting anywhere. My lecture notes are useless in that they don't ...