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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42 views

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 ...
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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 ...
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52 views

Arbitrage argument with bonds

Let $B(t,T)$ denote the cost at time t of a risk-free 1 euro bond, at time T. Assume that the interest rate is a deterministic function. Show that the absence of arbitrage requires that: $ B(0,1) B(1,...
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How to model the different returns of agents with different information information

For a seminar, I would like to graphically represent the returns made by agents of different information standpoints. In other words, say I have a market tuple $(\Omega, \mathbb{F}, P,S)$ where $S$ is ...
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96 views

European Call option combined with Short selling

How would I calculate the abitrage profit from a combination of buying the $10 European call option and short selling X number of shares at t=0 and the coming out with a profit at expiry no matter ...
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83 views

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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62 views

Arbitrage strategy one-period model

Consider a one-period model with a stock $S_0=1$ and $S_1>0$. Introduce call options with strikes $K_1<K_2<K_3$ maturing at $T=1$. Assume further that $$ C(K_2)>\frac12(C(K_1)+C(K_3)) $$ ...
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45 views

Issue involving arbitrage conditions

In my book it's written that if one of these two conditions is verified then you can make an arbitrage. The two conditions are: $$1) \left\{ \begin{array}{c} \mathbf{q} \bullet\mathbf{n} \le0 \\ \...
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142 views

value of forward contract at inception

I am reading a derivation of the forward price $F$ of a forward contract. I think the author uses a circular argument to assume that "the value of the forward at inception is equal to 0" because the ...
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233 views

Interpretation of drift parameter $\mu$ in GBM

Currently studying Ito's calculus. Looking on the GBM model: $ \frac{d S_t}{S_t} = μ dt + \sigma d B_t$ we end up on the expected stock price at time t: $E[S_t]=s_0 e^{\mu t}$.What does actually $\mu$ ...
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292 views

How to show arbitrage when a European option price is greater than the no-arbitrage price?

My example is: Current price = 20, If it goes up it'll be worth 22, if it goes down it will be worth 18 risk free rate: 12%, time = 3 months Strike = 21 call option is worth 0.633 I know that if the ...
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62 views

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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167 views

Isn't this modified stop-loss strategy an arbitrage?

In John Hull's The Book, section 18.3 he briefly discussed a stop-loss strategy for writing a call option: buy one share of stock whenever $S_t>K$ and sell it otherwise (except at time $0$: if $S_0\...
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31 views

Best strategy for generating floats with minimum amount of risk

I'm looking for a way to get cash-in-hand in exchange for future obligation. For example, I can sell deep-in-the-money puts and buy out-of-the-money puts (for hedge) with expiration of 2 years, The ...
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398 views

How to calculate an option porfolio cost and payoff function?

There are call and put options on the same underlying asset, with the same expiry, $T$, and with strikes $K_c=(k_c^1, k_c^2, \ldots, k_c^m)$ and $K_p=(k_p^1, k_p^2, \ldots, k_p^m)$, $S_t$ is a price ...
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108 views

possible to estimate if hard-to-borrow?

I'm building a low frequency US equity stat arb system. On any given day the system is long ~100 stocks and short ~100 stocks. It trades once a day at the open, and on average 4/5 of the portfolio ...
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127 views

Black Scholes: two assets, same $W$-process

Consider a Black Scholes model with two risky assets that are driven by the same $W$-process, and then 1 risk-free asset. When is this model arbitrage-free and complete? We have only 1 driving ...
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268 views

Probability and statistics in Quantitative Finance

Certain types of traders attempt to repeatedly buy and sell the same asset for a profit over a short time period, such as high-frequency “market makers”. For example, if you can repeatedly sell a ...
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406 views

If I am very fast (less than 10 microseconds latency) what would be the first strategy to execute? [closed]

Let's assume I found the holy grail of low-latency trading (which I didn't). For educational purposes, what would be the first strategy I would direct my trading code?
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117 views

Options conversion/reversion arbitrage [closed]

I'm trading bitcoin option and i'm trying to find arbitrage opportunity with a synthetic short/long and a long/short future position. The options are europeans style and settled in BTC. The contracts ...
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238 views

Replicate by Arbitrage price of a forward

Given market(Mid): 1- USD Swap market (fixed for float). Float leg pays 3MLibor quarterly, act360. Fixed Leg pays annually, act360. Market is trading mid at 1.125%. 2- TIIE market. Fixed for ...
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1k views

Calculating arbitrage- S&P 500 stocks vs S&P 500 Index future?

How exactly would I go about investigating whether the S&P 500 stocks were currently over-valued compared with the price of the S&P 500 Index futures contract? Is it just a case of taking each ...
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2k views

What software should I use for forex arbitrage?

These are my requirements: Speed of lookup & update Speed of crunching large numbers and combinations The exchanges I want to connect to will mostly provide json feeds to their orderbooks & ...
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102 views

Option Arbitrage Opportunity [closed]

Could you please explain me whether there is an arbitrage opportunity in this situation (added below)?
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315 views

How to calculate riskless profit out of call options?

I'm having trouble with working out a question that I can't currently ask my lecturer as they're away. Hoping for some help here with why the answer is (a). A stock price is currently \$40. It is ...
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129 views

Implicit relation between risk and reward

I want to differentiate w.r.t. $\sigma^2$ the following equation $u'(Y)\mu$ + $\frac{u''(Y)}{2}$$(\sigma^2 + \mu^2) = 0$ where we can consider $\mu$(reward) as an implicit function of $\sigma^2$(risk) ...
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1k views

Tutorial for working with tick data? [closed]

Can you recommend a good tutorial for working with tick data for the purpose of algorithmic trading? Is the data normally stored in a database and only bits are read into memory at a time? Is there ...
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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 ...
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4k views

Show that convexity of call price as a function of the strike is violated [closed]

European call options with strikes 90, 100 and 110 on the same underlying asset and with the same maturity are trading for 22.50, 18.84 and 13.97 respectively. show that the convexity of the call ...

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