Questions tagged [derivatives]

A financial contract whose payoff is linked to the evolution of an underlying security.

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0answers
135 views

Martingale approach - Option pricing with Radom-Nikodym

I would like to get the price of an option which pays at time T the minimum between the logarithm of (S(1,T) / S(1,0)) and the logarithm of (S(2,T) / S(2,0), with the following processes: (The two ...
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406 views

Why does the price of a derivative not depend on the derivative with which you hedge volatility risk?

I'm trying to derive the valuation equation under a general stochastic volatility model. What one can read in the literature is the following reasoning: One considers a replicating self-financing ...
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1answer
1k views

Local Volatility implementation

The Dupire equation is well-known and mentioned in thousands of articles. Although I could not find a lot of documentation about a consistent and proper way of implementing the formula (The difficulty ...
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82 views

Structured Energy Option Pricing

Let's say I have an option with the following terms. This is for an energy product (ie natural gas) The contract will last for 6 months The payoff is the difference between the first of month index ...
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2answers
840 views

Contingent claim and Derivative

What's the difference between a derivative and a contingent claim? What is an example of a derivative which isn't a contingent claim? Since options or swaps are examples of derivatives that are ...
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2k views

Cash-settled swaptions

I was wondering, what is the motivation behind the payoff of the cash swaptions being multiplied by the swap annuity? $$c(S_{\theta, T})=\sum_{i=\theta+1}^{T}\tau_i\frac{1}{{(1+S_{\theta,T}(\theta))}^...
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697 views

Multi-currency CSA discounting curve construction

I have a number of eur/usd and gbp/usd MtM Basis swaps that are collaterized in USD. For the non-usd legs I'm constructing the muti-ccy csa discounting curve. Im using forwards for the short end of ...
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1answer
196 views

Rebasing of Cap Volatilities

I recently found this article where towards the end the author describes a method to rebase cap volatilities. Their method works like this: for a fixed strike assume that you are given the implied ...
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2answers
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What would be the issue price of the following contract?

Stock currently A has a price equal to 100. Stock B also currently has a price of 100. The contract has a maturity $\mu$ of one year. At maturity the payout is the max price of either A or B. What is ...
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1answer
165 views

Black 1976 caplet value

I've seen from two sources different formulas for the caplet value (Black 1976): $$Caplet_1 = N\cdot DiscountFactor_{0,k}\cdot yrFrcn_{k,k+1}\cdot [F_{k,k+1}\cdot N(d_1) - R_k\cdot N(d_2)]$$ $$ ...
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973 views

Use of cap volatilities

I have a cap volatility surface for the 6 months Libor. Can I use the same cap volatility for every cap's caplet to valuate the full cap? Example: Valuate a 18M cap (Libor 6M) by valuating 3 6M ...
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245 views

To what degree does computational complexity affect the pricing of options?

I have been tasked with writing a 25 page paper on computational complexity. The first 10 pages of this should be background an introduction to the field (which I have largely done already) and the ...
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1answer
836 views

Theoretical limits for contango and backwardation

What do you think would be the theoretical limit for contango? What about backwardation? This was asked in an interview. I am still not so sure about the answer.
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264 views

How do I value uncollaterised swaps?

Do I need to discount using the OIS curve? Then add some sort of FVA adjustment over and above the CVA/DVA? How do I work out a banks cost of funding? Any help would be greatly appreciated. ...
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1answer
515 views

Books about Monte Carlo Simulation on derivatives with Python

I am looking for a good reference for Monte Carlo simulation applied to derivatives with Python. Most books I found until now deal with C++... I have found "Derivatives Analytics with Python" by Yves ...
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1answer
956 views

Fixing date, start date, end date in interest rate derivative valuation?

I was reading a technical report by Hagan, which can be downloaded here on the valuation of accrual swaps and range notes. It caught my attention that in the valuation he comments this: Consider ...
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1answer
128 views

Books/papers on Insurance Derivatives?

I am looking to learn more about insurance-linked securities. I work for an insurance company and am interested in catastrophe risks and cat bonds. I have a good statistical background and master-...
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1answer
442 views

Pricing of a derivative using Risk Neutral Valuation.

I am new to option pricing and following problem came up that I don't understand how to handle. A derivative will pay out dollar amount equal to $$\frac1T\ln \frac{S_T}{S_0}$$ at maturity, where $...
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2answers
4k views

What is the difference between funded and unfunded derivative?

What is the difference between funded and unfunded derivative? Can anyone explain the difference between these two?
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1answer
115 views

Calculating expected loss using actual probabilities

I'm calculating expected loss on fixed-income using actual default probabilities and risk-free rate as the discount factor. I understand this is not theoretically correct. In absence of risk-neutral ...
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2answers
410 views

Pricing 0% interest rate Floor Black Model

I'm having some trouble pricing a 0% interest rate Floor following Black's formula. The term d1 contains the expresion Ln(Forward/Strike) if the strike is exactly 0 this expresion yields an ...
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1answer
220 views

How to price up-out-call by solving heat equation like down-out-call

We know that by changing the variables we can obtain the Black-Scholes formula of vanilla call through solving the ...
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2answers
443 views

The dice game and derivatives trading

I happened to a interview question: Give a equal dice, you will gain the money which is the number you roll, then how much will you pay for the game. Naturely, the answer is 3.5. But the interview ...
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1answer
323 views

Binary option analytical formula

Given $r=0$, $\sigma(K)=\text{const}$ and: $$ \text{Binary} = \lim_{ε → 0} \frac{(C(K,\sigma (K))-C(K+ε,\sigma(K+ε)))}{ε} $$ I have to find the analytical expression for the above. Since $σ(K)=\...
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1answer
366 views

Number of Time Steps in Binomial Option Pricing - Problem?

I am trying to price a digital option and the final price under different number of time steps are as follows: Is it possible to have a graph like this?
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1answer
577 views

at-the-money short term straddle and the implied vol

Here is a passage from "Advanced Equity Derivatives: Volatility and Correlation" by Sebastien Bossu, Wiley (2014). We see the prox $\beta_0,$ it seems to use the approximation that ...
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1answer
208 views

eurodollar future

I just found out about eurdollar futures and I am confused. A eurodollar future contract is defined as a cash settled future based on a Eurodollar Time Deposit having a principal value of USD $1,000,...
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2answers
978 views

Pricing Cancelable swap

Consider a first hypothetical, a swap. Party 1 is paying 6 month Libor, semi-annually. Party 2. pays $1+3*(\frac{Index_\color{red}{T}}{Index_0}-1) $ only at maturity. Say the notional is 1. $Index_t$ ...
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349 views

Refer some most recent books of derivatives pricing by C++

Could you refer some most recent books of derivatives pricing by C++ including Tree method, Finite difference method, Monte Carlo etc. Once I read a series of <...
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0answers
172 views

Pricing of Swaption by Proxy and Monte Carlo

here's the problem. Suppose you want to compute the price of a Call option on a Swap contract. Let $T$ and $T+S$ the times (in year fraction) where the Swap lives and suppose that the fluxes of the ...
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1answer
714 views

Log-moneyness definition [closed]

Define the time-0 log-moneyness of a call on stock $S$ with strike $K$ and expiry $T$ to be: $$\log(S(0)\exp(rT)/K)$$ What does it mean for the strikes K to be at-the-log-moneyness?? I guessed this ...
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1answer
151 views

IVF and implied distribution of underlying in John Hull's book

There is a statement in John Hull's book Options, Futures and Other Derivatives 9th page 633 for the relation between ...
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1answer
83 views

Cash as Collateral in OTC Market

In OTC market Collateral Posting as cash is normal, so when it is said Collateral Posted as USD CASH Does that mean Actual amount of currency is posted electronically (or any security is posted) ...
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2answers
311 views

How to make the arbitrage if intrinsic value is greater than European call value

It always says if the intrinsic value is greater than European call value, there will be a arbitrage opportunity,but how to construct the portfolio $(S_t - K)^+$ or how to make this arbitrage. By the ...
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1answer
167 views

What are good risk management books or docs? [duplicate]

I have an unusual request/question. I was wondering if anyone here could recommend me some books about risk management and equity derivatives. I am about to do an internship as a risk analyst on an ...
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1answer
266 views

Replicating a square derivative with calls and puts

I have a derivative that pays off $S_T^2$ at time $T > 0$ with $S_T$ denoting the price of a non dividend-paying stock at $T$. I came across a question about how one can statically replicate this ...
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1answer
561 views

quanto adjustments

Here is quanto adjustments in John Hull's book Options, Futures and Other Derivatives 9th ...
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1answer
162 views

Zero value of cash flow for future in Shreve's book

Here is the statements of future price in Shreve's book Stochastic Calculus for Finance II page 244 to proof the ...
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1answer
2k views

What is CVA (credit valuation adjustment)?

According to Wikipedia, CVA is defined as the difference between the risk-free portfolio value and the true portfolio value that takes into account the possibility of a counterparty’s default. What ...
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1answer
1k views

How to measure contango?

Is there any unit of measure for the magnitude of the contango (or backwardation) for futures, so you can compare the contango of many symbols.
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1answer
137 views

How to understand closing position of futures

When we want to close out the position of futures prior to the delivery period, you will entering into the opposite trade to the original one. Equivalently, except ...
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1answer
210 views

Physical Measure in Weather Derivatives — Hull

In Hull's 8ed., he states in Chapter 33, Energy and Commodity Derivatives, The second part of the chapter considers weather and insurance derivatives. A distinctive feature of these derivatives ...
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1answer
2k views

What exactly is a deposit futures contract?

I have been working with Deposit Futures and the Brazilian One-Day Interbank Deposit Future but I can't get my head around them. What exactly is delivered and when? What is the contract a right to?
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1answer
314 views

Replicating a portfolio with a certain payoff function

Assume there are two stocks $S_1$ with price $p_1(t)$ and $S_2$ with price $p_2(t)$ where $t$ indicates time. Assume, there is a hypothetical derivative $D$, which is such that, price of $D$ at a time ...
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1answer
193 views

How do I modify my basic black scholes model in Excel to price american options?

I've modeled a basic black scholes model in Excel and I have been using it to price European options for backtesting purposes. This has been working fantastically and I would like to adjust this to ...
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The interpretation of discounted Greeks

I understand that Delta measures the rate of change of the theoretical option value with respect to the change of the underlying asset price. This also represents the number of shares a call option ...
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1answer
147 views

Reference for why a derivative is a derivative and not say an insurance contract

I recently spoke to an options trader that tried to demonstrate option pricing by considering a random walk of balls dropping down a lattice so the underlying stochastic process is a simple random ...
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1answer
82 views

CDS for Funding

I was wondering if anyone is familiar with how credit default swaps can be used for corp funding and financing. I came across an old case where a bank created a funding structure for a client (asset ...
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1answer
93 views

Is there a way of synthetically deleveraging a Real Estate portfolio?

If I manage a Real Estate portfolio with approximately 400 million in debt, which is roughly 50% Loan-to-Value (the properties are worth about 800 million). Is it possible to synthesize a bond ...
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1answer
383 views

Pricing the Passport option

Suppose underlying asset $S$ $$dS = \mu Sdt + \sigma Sd W$$ our portfolio $\pi$ consist with $q(t)$ stock $S$ and cash $\pi - qS$...

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