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1answer
30 views

Mathematically: How does increasing the number of assets reduce idiosyncratic risk?

As part of an Asset Pricing Module I'm currently taking, whilst looking at APT Ross (1974), we looked at how according to this model, risk originates from both systematic and idiosyncratic asset ...
0
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1answer
77 views

“For any random variable $X$, someone will be willing to buy and someone to sell a financial instrument, whose final payoff is $X$.”

we will assume that for any random variable $X:\Omega\rightarrow\mathbb{R}$, some investor will be willing to buy and some investor will be willing to sell a 'financial instrument' whose final ...
-1
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1answer
60 views

European option on a dividend paying stock, limits to arbitrage?

What is the price C of a European call option on a dividend paying stock? I believe it is: C = U. N(d1) - exp(-rt).K.N(d2) d1 = [ ln(U/K) + (r + v^2/2).t ]/[ v.sqrt(t) ] d2 = d1 - v.sqrt(t) U ...
5
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0answers
182 views

Integral-differential equation for forward rates

I am struggling in this question: Let $P(t,T)$ denote the price of a zero-coupon bond (with marturity at time $T$) at time $t \in [0,T]$. As usual, at time $t$ for maturity $T$, the forward rate is ...
5
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0answers
170 views

Arbitrage free price of a derivative when the price is collected over the lifetime of the derivative

Let $X_t$ be an american style financial derivative with random exercise time $T$ where $t$ and $T$ belongs to some finite set $A$. Buying this derivative requires the buyer to pay $p_t$ up to time ...
2
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0answers
46 views

Show that in an arbitrage-free and non-redundant market a certain set is compact

Some notation: We consider a financial market with $d+1$ assets, the $0$-th asset is considered the risk-free asset, the others are the risky ones. The vector $\overline \pi \in \mathbb R^{d+1}$ ...
2
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0answers
120 views

Simple Forward Interest Rate Proof

Just trying to check my logic here: Let $Z(t,T)$ be a Zero-Coupon Bond with maturity $T$ bought at time $t$, $S_m$ be the spot interest rate for time $m$ and $S_n$ for time $n$ respectively, where $n ...
2
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0answers
188 views

Stochastic discount factor (aka deflator or pricing kernel) and class D processes

When (under what assumptions on the model) does a Stochastic Discount Factor need to be of Class D? What would be the implications if it was not? Is it connected to one of the no-arbitrage notions?
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0answers
29 views

HJM model, existence of arbitrage:

The Setup: Suppose I know the yield curve of a Bond satisfies: f (0, t) = 0.04 for t ≥ 0 and f (ω, 1, t) = 0.06, t ≥ 1, ω = ω 1 , 0.02, t ≥ 1, ω = ω 2 , where Ω = {ω 1 , ω 2 } with P[ω i ] > 0, i = ...
0
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0answers
26 views

Deriving the yield curve from the HJM dynamics

If I know that my model follows a no-arbitrage HJM model: \begin{equation} df(\tau) = \left(\sigma(\tau)\int_0^{\tau}\sigma(u)du\right)dt +\sigma(\tau)dW_{\tau} \end{equation} (where $\tau:=T-t$, ...
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0answers
47 views

Market with exponentially distributed random variable

Consider a market consisting of a stock with $S_0^1=1$ and $\log(S_1^1)=Z$, where $Z$ is an exponentially distributed random variable. $S_0^1$ denoted the prices of the stock $1$ at time $t=0$ and ...
0
votes
0answers
21 views

Bond's bid-ask spread with no arbitrage assumption

Suppose I have a bond with unknown bid-ask spread, and a portfolio, containing it and also other bonds, all with known bid-ask spreads. How can the unknown spread be inferred? I assume there should ...
0
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0answers
19 views

Stochastic correlation arbitrage-free replication

I'm interested in possibility of stochastic correlation arbitrage-free replication (something VIX-style, mayby). To my knowledge, no such method exists. Could you provide some intro to the problem: ...