Questions tagged [numerairechange]

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American Perpetual Put Option

I want to compute the expected payoff of a (classical) perpetual American put option in the Black-Scholes-Merton (BSM) framework with an optimal strategy of exercising the option at time $\tau=\inf\{t:...
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51 views

Change of measure for BGM (LMM) Model

I've been checking the demos for BGM (LFM) forward rate model. Here's a short reminder to help you follow: Now, take the following $$\frac{dL_j(t)}{L_j(t)} = \sigma_j. dW^j(t) = \mu_{ij} dt + \...
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32 views

Discrete term structure models - generalized procedure to ensure positive probabilities across multiple measures

Question: Is there a generalized procedure for building a discrete (e.g. binomial) term structure model with risk-neutral branching probabilities that ensure positive probabilities under alternative ...
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153 views

Dividend paying asset, why can't be taken as numéraire?

Why when considering numéraires, one cannot use a dividend paying asset to define a risk neutral measure? Here's where I got my question : (Shreve - Stochastic Calculus For Finance II)
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78 views

An arbitrage strategy involving forward contracts to show that LIBOR rates are martingales

I note $L_{t}^{[T_s, T_e]}$ the forward rate at time $t$ for the period $[T_s, T_e]$. Recall it is the strike making equal to $0$ the value at time $t$ of a forward contract for the period $[T_s, T_e]$...
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45 views

Expectation of expression with two currencies under forward measure

I'm trying to calculate the expected value, at time $0$, of a cashflow paid at time $T$, resetting at time $t$. The coupon is of the form: $V_0=\mathbb{E}^{T_2}\left[\frac{A_t^y(T_1,T_2)}{B_t^x(T_1,...
2
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145 views

Value of an option to exchange an asset for another

I'm working out the examples in the paper "Changes of Numeraire, Changes of Probability Measure and Option Pricing", corollary 3. An option of exchanging asset 2 against asset 1 at time T, its time-0 ...
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29 views

In a multi-curve context which numéraire is used to change to the payment probability of a forward asset X paid at time T?

Should it be the coupon associated to the funding curve of the asset? Thanks.
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107 views

Hull Martingales and measures problem 27.16 7e?

Here's a question from Hull's Options Futures and Other derivatives which I'd appreciate if someone helped me to clarify. The question is from the chapter "Martingales and Measures" Suppose that the ...
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169 views

Effect on variance of change of measure

My current understanding: (a) changing the probability measure of a diffusion process does not change the variance. (b) for a general stochastic process the variance may change. Please confirm whether ...
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1answer
48 views

Arithmetic Asian Option

Assume the risk-free bond Bt and the stock St follow the dynamics of the Black & Scholes model without dividends (with interest rate r, stock drift $μ$ and volatility $σ$). Let $A_T:=\frac{1}{T}...
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34 views

Change of numeraire/probability when asset pays dividends

So I was looking at Margrabe's formula for exchange call options in the book 'Mathematical Methods for Financial Markets' (Jeanblanc, Chesney, Yor), and I was having trouble justifying their change of ...
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43 views

Risk neutral measure & change in numeraire

There are two questions about risk neutral and change in numeraire I am not so sure if my answer is correct. Question 01: Risk neutral Let says I have 2 risky asset A and B. Each has stochastics ...