# Questions tagged [no-arbitrage-theory]

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### Pricing weighted/average stock price claim

In a market consisting of a bank account with a constant interest rate r and a non-dividend paying stock S, consider a T-claim that pays $X = S(T)/S(T_0)$ at time T, where $T_0 < T$. a) ...
3k views

### How are the two concepts No arbitrage & Risk neutral probability related?

The title, and might I add, that this question is in relation to the Black-Scholes model and why the concepts are important for option pricing in general.
883 views

### How to understand the no call or put spread arbitrage condition

The book Advanced Equity Derivatives Volatility and Correlation page 22 said To preclude arbitrage we must at least require: ...
117 views

### Pricing and Arbitrage of Inverse Asset Claim

I'm working through the following little exotic exercise and have some questions and curiosity as to whether I'm on the right track Consider the claims $$Y_t=\frac{1}{S_t}$$ $$X=\frac{1}{S_T}$$ a) ...
654 views

### Pricing when arbitrage is possible through Negative Probabilities or something else

Assume that we have a general one-period market model consisting of $d+1$ assets and $N$ states. Using a replicating portfolio $\phi$, determine $\Pi(0;X)$, the price of a European call option, with ...
239 views

### Do underlying assets have a no-arbitrage price?

Can it be shown that the Fundamental Theorem on Asset Pricing (FTAP) applies to underlying assets -- namely bonds, equities, and commodities? FTAP says that assets have no-arbitrage prices equal to ...
942 views

### Why does arbitrage free imply complete market?

Proposition 2.10 of Tomas Bjork's "Arbitrage Theory in Continuous Time" states that if the general binomial model is free of arbitrage then it is also complete i.e. every contingent claim has a ...
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### How realistic are the scenarios outlined in my course?

I am currently taking a course in Financial Mathematics as part of my Maths degree. Many of the covered topics are quite basic, and revolve around potential arbitrage opportunities. For example, ...
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### Option price in a neutral risk world is the same as in the real world. I can not understand! [closed]

Good evening. I know there are several posts on the subject but unfortunately I can not fully understand this concept and I hope you can help me. To price the option the fundamental assumption ...
113 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 = 1,...
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### Arbitrage problem [closed]

Question A share of non-dividend paying stock is trading at USD 30. The maturity of both options is 1 year from now. A put with a strike of USD 28 is trading at USD 1 and call with a strike of USD 29 ...
891 views

### No-arbitrage theorem: a proof

The market is arbitrage free iff there exists an equivalent martingale measure for the discounted price process of the stock. My course only provides me part of the entire proof that shows that ...
311 views

### Fair price and no arbitrage

The market is arbitrage-free iff there exists an equivalent martingale measure for the discounted price process of the stock. So in a world with a finite amount of possible outcomes $\Omega$ that ...
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### Concatenation property of a set of semimartingales

Consider as in (1, Definition 2.1) a convex subset $\mathcal{X}_1$ of the set of semimartingales $\mathbb{S}$ satisfying the following properties: $X_0=0$ $X_t\geq -1$ for all $t\geq 0$ for all ...
528 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 ...
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### “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 payoff ...
160 views

### What is the principle of determining an arbitrary option price

First I want to talk about one of my wrong ways of pricing an European call option. When I consider the simplest case of European call option, the first idea of determining the price is to calculate ...
5k views

### Simple value of a Forward contract at an intermediate time question

I am taking "Financial Engineering and Risk Management Part I" from Columbia University on coursera and I got a seemingly simple question wrong on the first quiz. This is all based on the no-arbitrage ...
945 views

### American Option Bounds with Dividend Yield

What are the upper and lower bound of American call and put options for an underlying with continuous dividend yield? For European options, the bounds are known as \begin{align*} [S_te^{-d\tau}-Ke^{-...
409 views

### Understanding the HJM drift condition's dimensions

In an HJM model the forward rate dynamics follow $$df_t(T) =a_t(f_t(T))dt+b_t(f_t(T))dW_t$$ where $W_t$ is a $d$-dimensional brownian motion, $b_t$ takes values in $\mathbb{R}^{d\times d}$ and $a_t$ ...
433 views

### Risk neutral pricing - Example from a book is correct?

I found the following example in a book on Model Risk, while trying to explain how risk-neutral pricing takes properly into account the risk involved in different investments. The Example is this. ...
449 views

### Solving for r in the Black Scholes equation

Could you please correct which parts of my reasoning are wrong? Let's suppose that I know for sure that my estimate for a stock volatility is right (I have a crystal ball) and that it will be for ...
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### 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 ...
344 views

### arbitrage proof question

prove the condition $D<R<U$ is equivalent to the absence of arbitrage: R = risk free investment rate of return. U and D are returns corresponding to the upward/downward price movements of a ...
352 views

### What is the arbitrage opportunity in this simple one-period market?

I have a single period market, and three states, and I have 3 risky assets. I assume no interest. So I have three states $\Omega=\{\omega_1,\omega_2,\omega_3\}$. All assets start with the value 1, ...
124 views

### option time value in the pricing models

option price = intrinsic value + time value where intrinsic value (in other words payoff at N) is defined generally as difference between the underlying asset price and strike price (order depending ...
158 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 $\tau:=T-t$, ...
442 views

### Prove arbitrage opportunity

The continuously compounded interest rate is $r$. The current price of the underlying asset is $S(0)$ and the forward price with delivery time in 1 year is $F(0,1)$. Short selling of the stock ...
I am reviewing the steps of proof that the binomial model is complete and don't understand the marked in red transition. Could anybody explain this step? If $P^{**}$ is a risk-neutral measure, so ...