-1
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1answer
110 views

Option Pricing, A Practitioners Guide, Martingale's, Drift Change and Radon-Nikodym

Im slightly confused about this section of the booklet regarding option prices byIain J. Clark. 1) Regarding the part of obtaining a martingale property we require that the last exponential term ...
0
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0answers
83 views

Jump diffusion process with sum of Poisson processes a martingale?

Hi Mathematics community, assume you have dynamics of a jump diffusion process consisting of a Brownian motion and a sum of compensated (not necessarily independent) Poisson processes, i.e. ...
1
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1answer
84 views

Stochastic differential for general semimartingale

By using the canonical representation of a semimartingale in Eberlein, Glau and Papapantoleon: "$H = B + H^c + h(x) \ast (\mu − \nu) + (x − h(x)) \ast μ$ where $h = h(x)$ is a truncation ...
1
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1answer
769 views

Easy proof of Black-Scholes option pricing formula

I use this Book to read the option princing in Black-Scholes model in pages 93-99, The poof of the formula given by $$c(s,t)= N(d_1(s,t)- Ke^{-rT}N(d_2(s,t)))$$ where $$d_{1,2}=\frac{\ln(s/K)+(r\pm ...
2
votes
1answer
145 views

Is the following a martingale?

Let $X_{n}$ be a martingale with respect to a filtration $\mathbb{P}_{n}$. Define: $Y_{n}$ := $X_{n}^{3}$ Is $Y_{n}$ a martingale? Supermartingale?
2
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0answers
73 views

Doob Decomposition of American Option

I am trying to figure out the Doob decomposition of an American put option in a discrete time binomial model. I know how to price the American put, but I'm having trouble expressing it as the sum of ...
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0answers
95 views

Compactness of the set of densities of equivalent martingale measures

Consider an incomplete market $(\Omega,\mathcal F,\mathbb P)$ driven by a semimartingale $S=(S_t)_{t\in[0,T]}$. Under the no free lunch under vanishing risk (NFLVR) assumption, the set $\mathcal ...
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1answer
714 views

brownian motion-proof of Martingale

Can anyone help me with the following problem? Let $W(t), t\geq 0$ be a Brownian motion with filtration:$F(t)$. Let $0\leq s\leq t$. 1- Show that $E\left [ W^{3}(t)\mid F(s) \right ...