# Questions tagged [arbitrage]

The simultaneous purchase and sale of a financial security in order to profit from the difference in the security price during the trading activity.

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### Black-Scholes pricing of european call option

I am really confused on the usage of the greeks and the Black-Scholes model for option pricing. To gain some more understanding I am attempting to see if I can price a european call option under the ...
1answer
95 views

### Arbitrage strategy using binomial tree

Suppose that we have a one step binomial tree model for a company. Lets say that the time per step is T, and that price of the stock can go up to $p_1$ or go down to $p_2$. Suppose a T-month European ...
1answer
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### Hedging With Zero Coupon Bonds from The Concepts and Practice of Mathematical Finance by Mark Joshi

In section 2.5 he describes an example of arbitrage-free pricing (attached below). I have a pretty solid understanding of how we arrived at $K' = K\frac{1+d}{1+r}$, but I got a little lost when he ...
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### Modelling considerations for a jump model

The Problem: Suppose I have a simple jump model for an asset price $$dS = S(t-)[\mu dt + YdN(t)]$$ where $N(t)$ is a Poisson process and $Y_i$ are the jump sizes (assume independece of $N(t)$ and ...
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### Hedging/Arbitrage with multiple period binomial tree

Plenty of material is written on how to hedge/arbitrage option price in one period binomial model, but I cannot find anything about hedging in multiple periods. If one to use multiple periods binomial ...
1answer
94 views

### Put-Call parity arbitrage relationship

I would like to know what the relationship is between the time value of call/puts. From the put call parity formula $$C-P = S_{t} - PV(K)$$ and that value of call/put options is simply the sum of ...
0answers
28 views

### No unique no-arbitrage price when the stock price can remain unchanged

In a 1-period binomial model, with initial stock price 100, if the stock price is either 50,100, or 150 after 1 period then how can I show there is no longer a unique no-arbitrage price for a European ...
2answers
94 views

### Tips on building an automated trading system in python [closed]

I have an trading API that allows me to send/cancel/update orders. I have marketdata that I can use through another API that gives me orderbook data. Now let's say I want to build a simple arbitrage ...
2answers
307 views

### Would C++'s speed over Python make it a more applicable language for scalping arbitrage opportunities?

I am using the Bittrex exchange API to ping markets to poll whether there are triangular arbitrage opportunities available for USD/BTC/LTC/USD. Note that I am not trading but rather synthesising them ...
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### What market conditions are attributable to prolonged instances of triangular arbitrage opportunities?

I am investigating the potential for intra-exchange triangular arbitrage opportunities for the Cryptocurrency market. I believe that due its immaturity, relatively low volume and high volatility that ...
2answers
173 views

### How to detect price anomalies in HFT?

Let's say I'm developing an HFT application and seeking arbitrage in futures markets between MAY contract(M) and JUNE contract(J). In this strategy, my spread is ...
1answer
194 views

### Relation of risk-neutral probability measures to arbitrage opportunities

Could someone describe how risk-neutral probability measures are linked to arbitrage opportunities and also to whether or not a market is complete? I've been asked this question and am unsure how to ...
1answer
92 views

### Arbitrage between American and European put options on the same underlying asset

Suppose there exist both American-style and European-style put options on the same underlying asset, at the same strike price, and with the same expiry date. Suppose the European put is selling below ...
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95 views

### How to find an arbitrage when the solution is not obvious (2 assets in a market)?

I am struggling to find an arbitrage in the following configuration. I know how to prove that there is an arbitrage (using the fundamental theorem of asset pricing). So I ve proven there is an ...
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76 views

### Are statistical arb and relative value arb strategies implicitly short volatility?

I obviously don't want to generalise here, but my initial impression of stat arb and relative value arb is that these strategies earn stable pennies during bull markets when volatility is depressed ...
1answer
73 views

### Is there a reason why futures and options have more substitutes than other financial instruments?

This is somewhat non-technical question, but it seems like this forum is still the best place for it. I'm reading Shleifer's Inefficient Markets, where he points out that [...] for futures and ...
1answer
98 views

### How to price complex corporate actions with spinoffs

Let's look at below UTX/RTN merger as an example: https://www.fool.com/investing/2020/03/30/raytheon-united-technologies-merger-gets-green-lig.aspx The merged companies will from that moment ...
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194 views

### Zero Volatility Options Pricing

Suppose an asset evolves in time according to the SDE $$dS = \mu S dt + \sigma S dW,$$ where $\mu>0,\sigma>0$ are fixed constants and $dW$ is a Wiener process. To price options for this ...
1answer
108 views

### Basic arbitrage exercise

In the exercise we are given, possible contracts to buy/sell and possibility to take credits / make deposits money with current market rates. We are asked if its possible to make profit at time T=0 ...
1answer
210 views

### Boundary for European Put Option

As an entry level financial engineer, I'm learning about call-put parity, which helps us to get the boundary for call option: $S-Ke^{-rT}\leq c\leq S$, what about put option? Should its upper bound be ...
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### Bond arbitrage in practice

If we have the following term structure for riskless bonds: \begin{array} {|c|c|} \hline \text{Maturity} & \text{\$1 Zero-Bond price}\\ \hline \text{0 years} & \$ 1.00 \\ \hline \text{1 years}...
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67 views

### Relationship between Calendar Spread Arbitrage and Probability Density Function (pdf)

We all know that the butterfly spread no-arbitrage condition can be expressed as an inequality restriction on the second-order derivative $\partial ^2C/\partial K^2 \geq 0$, which also means the ...
1answer
121 views

### Arbitrage opportunity between two call options with strike price \$40, \$30 and cost \$4, \$3 respectively?

Question: Given two call options $c_1$ and $c_2$ with strike price $30$ and $40$ respectively. If $c_1$ costs \$3 and$c_2$costs \$4, is there an arbitrage opportunity? My attempt: Short $c_2$ and ...
1answer
231 views

### A financial market is complete if and only iff there exists a unique equivalent martingale measure

Do you have any intuition behind the following theorem : A financial market is complete if and only iff there exists a unique equivalent martingale measure. I understand the easier version of ...
1answer
134 views

### theta for SPX options vs. E-mini future options

Interactive Brokers currently shows the following data for SPX options at strike 3000 and expiry 2020-09-17: calls: bid/ask 234.10/236.30, theta -0.362 puts: bid/ask 146.70/148.40, theta -0.225 Then ...
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### One periodic binomial model

I need to look into a one-period Binomial model $(B_t, S_t)$ with interest rate $r = 0.1$ , $S_0 = 100$ and $$S_t= 120 \, \text{with probability}\, 0.5$$ $$S_t= 60\, \text{with probability}\, 0.5$$...
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### Binomial Model - completeness in presence of arbitrage

Consider a uniperiodal binomial model where I buy one bond of value $B_0$ and rate $r=0.1$, and $h$ stocks with price $S_0=5$. The value of the portfolio at time $t=0$ is $$V_0 = B_0 + hS_0,$$ ...
1answer
648 views

### Why isn't the Vasicek model arbitrage-free?

Could anyone explain why the Vasicek model isn't an arbitrage-free model? Additionally, which interest rate model is arbitrage-free and why?
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### Law of one Price and Cointegration relationship

I have a question on the relationship between the law of one price and cointegration of (financial) time series. To set things clear I start with something simple: Suppose there is an unobserved "...
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### A relatively useless but fun question for quants and physicists

Suppose I am a trader travelling in a very fast spaceship. What kind of SDE and corresponding PDE should I jot down and work with in order to ensure that there is no arbitrage (or if there is ...
1answer
118 views

### Arbitrage-free IV surface definition vs. real arbitrage process

In the context of BS implied volatility surface fitting. In the literature, it seems that conditions for arbitrage are defined in a way that assumes that options can be traded at the same price for ...
2answers
124 views

### Using cumulative returns to hedge against the overall trend

I am curious about a hypothetical strategy where you are long for a given period (like a year), and at the same time you hedge against the overall trend by going short everyday and accumulating the ...
3answers
236 views

### Binomial model arbitrage

I've recently started studying math finance from Shreve's Stochastic calculus text. In the binomial model, there is no arbitrage $\iff d<1+r<u$. To show that no arbitrage implies $1+r<u$, ...
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### Arbitrage pricing models

I have been reading Wu's Interest rate modeling and in his chapter on the HJM model he says that With arbitrage pricing models, the prices of the basic instruments are treated as model inputs ...
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### Non-redundant asset?

I've been solving many exercises with three assets that have two possible payoffs each, one payoff per possible future state. The question is always the same, i.e. is any asset redundant. After ...
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### Factor model alternative? [closed]

Suppose there is a Fama-French model estimated for a stock of Shoemaker Ltd.: $α = 0.01$ $β_M = 0.9$ $r_M = 0.12$ $β_S = 0.3$ $S = 0.05$ $β_H = 0.2$ $H = 0.06$ $r_F = 0.03$ How would you ...
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29 views

### Possible interference of Cross-Rate inaccuracy and CIP Deviations

I am currently attempting to calculate historical deviations from covered interest rate parity between 2013 and 2018. I recently read that: "Unlike the interbank spot market, in the interbank ...
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### Definition Of A Portfolio

I have very recently started studying quantitative finance on my own through a book called An Introduction To Quantitative Finance by Stephen Blythe. In chapter 6 of his book, he sets out to prove ...
2answers
836 views

### Can someone explain rigorously Taleb's criticism of Nate Silver's election forecasting?

Taleb makes the claim in this paper (and others) that there exists some sort of bound on the variance of a binary forecast such that if a forecaster's binary predictions exceed the bounds on variance ...
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154 views

### Generalisation of calendar arbitrage condition to options on futures

This question has discussed the condition on which calendar arbitrage opportunities arise for European call options on a stock. Do similar criteria exist for European options on futures? The most ...
2answers
337 views

### Does high levels of vol-of-vol parameter in SABR lead to Arbitrage? (Something seems wrong with Hagans formula)

Main question: Do we need to restrict the vol-of-vol parameter in SABR further than $\text{vol-of-vol}>0$ and how do we determine the interval of vol-vol which the model is arbitragefree? ...
2answers
178 views

### Find arbitrage opportunity in the given market model

Consider the following 3-period-market-model: The discounted price of the risky asset $S$: How can I find an arbitrage opportunity in this model? I know that there would be no arbitrage if we ...
2answers
212 views