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Questions tagged [derivatives]

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

2
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2answers
41 views

Arbitrage-free calculation of flat term structure out of normal term structure for e.g. pricing european options

since e.g. the Black-Scholes model requires a constant interest rate (flat term structure) but the real world often has normal term structure, I was wondering if it is mathematically correct to ...
0
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2answers
40 views

how to derive the cost of carry formula

Can anyone explain why the cost of carry formula looks like this: $$F_0 = S_0 \cdot e^{(c-y)T}$$ ,where $S_0$ equals the spot price when $T=0$, i.e. today. $c$ denotes the cost of carry and $y$ the ...
2
votes
2answers
105 views

How is volatility different from variance?

I always thought volatility was just variance ^ (1/2). Now I'm reading this book and it's saying that the two are different concepts. Excerpts include: Partly due to its use in Black-Scholes, ...
1
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0answers
31 views

Monte Carlo VAR with differente asset classes

I have found a very useful post regarding the use of Monte Carlo simulaton to obtain portfolio Value at risk, based on Cholesky decomposition, random variates, etc. This post I'm talking about is: Is ...
4
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1answer
48 views

Discounted asset price is martingale in BS model

I want to verify that the discounted stock price process $\mathrm{e}^{-r(T-t)}V(S_t,t)$ is a martingale in the BS-model. Using Ito's formula and the BS-PDE I get that $$ \mathrm{d}\mathrm{e}^{-r(T-t)}...
0
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1answer
81 views

Why can derivatives be viewed as a portfolio of the underlying and the riskless asset?

I am struggling with the statement: "Every derivative of the underlying can be viewed as a portfolio of the underlying asset and the riskless asset." Is this based on the put-call parity? Also I ...
2
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1answer
43 views

Variance Swap : dividends and rates

In a simplified world you can assume that the var swap is replicated by a continuous set of calls and puts and interest rates are equal to zero. So your PNL is only sensitive to the volatility. But in ...
3
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1answer
56 views

Determining cost of carry for a future in Euronext.com [closed]

A snapshot from the trading book of the CAC 40 futures, on November 5 2018, is: Using the book prices, how can I compute the cost of carry implicit in the November and December contracts? Please ...
0
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1answer
92 views

How is the performance measure computed here?

The image is from John C Hull Textbook titled Options, Futures and Other Derivatives ( page 407 - Ninth Edition). The table above was obtained after computing the delta of stock price, shares ...
0
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2answers
108 views

Proof Black Scholes Theta

I saw the following proof of theta in a paper I read, and I thought it looked pretty neat. Unfortunately I don't understand the step that they do. This is what they do: Now, I don't get how they go ...
1
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1answer
34 views

Static hedge forward swap using zero coupon swaps

I'm trying to create a static hedge for a forward swap using two spot starting zero coupon swaps (to prove that there is no convexity adjustment needed). Here are the instruments - Paying fixed in ...
2
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1answer
76 views

How are Interest Rate Swaps Quoted

Im not sure if this is the right place to ask this question or whether Personal Finance & Money would be a better place. Basically I know that initially interest rate swaps are quoted based on the ...
1
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0answers
70 views

Cash-or-nothing and Asset-or-nothing price derivation

I was wondering how to derive the price of a cash-or-nothing and asset-or-nothing option by trying to work out the expectation under the risk-neutral measure, while assuming that the underlying ...
0
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2answers
52 views

Why can a deterministic portfolio only grow at risk free rate

In black scholes derivation we assume that portfolio grows at risk free rate because the process is deterministic, my question is why is it riskfree rate? If i have information about some event in the ...
0
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0answers
29 views

Arbitrage and state price formulation

I must be missing something really obvious due to my temporary obtuseness. Can someone please help me see the obvious? :-P Thank you. I am just browsing Darrell Duffie's Dynamic Asset Pricing Theory. ...
3
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1answer
88 views

The positivity of the market price of risk

Does the market price of risk, be it of stochastic volatility, interest rate or equity return, have to be positive? What is the rationale if it does?
2
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0answers
84 views

Exotic derivatives - Replication

I would like to replicate the payoff Max(0, Min(S1, K) - S2) with a combination of the following derivatives: -> option on S1, strike of our choice -> option on (S1-S2), strike of our choice -> A ...
3
votes
1answer
169 views

Quantlib derivative valuation from zero curve

I have newly started with Quantlib-Python for valuing derivatives. In all the examples stated in this bolg or in other places, market quote is inserted and bootstrapping is done via individual rate ...
2
votes
1answer
66 views

Which of the following derivatives are protected from arbitrary corporate action?

Practically speaking, are individual stock futures/options and Index futures/ (options on futures) protected from arbitrary company action? Say, in the extreme, all companies suddenly pays huge ...
3
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2answers
302 views

Pricing Corridor Variance Spreads

Recently in the equity derivatives market there have been some trades on what are known as "Corridor Variance Spreads." The large equity derivative dealers and investment banks have been promoting it ...
0
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1answer
91 views

uncollateralised otc derivatives and bank funding costs

I've read multiple references that imply that the valuation of OTC derivatives being related to bank funding cost. Given that an uncollateralised OTC derivative needs no funding from the bank's ...
0
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1answer
176 views

Is Red Code unique per derivative instrument

Does RED Code (="Markit Reference Entity Database Code") uniquely identify the derivative that has been traded? Is it possible to get a derivative's ISIN code from RED Code?
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1answer
27 views

Futures Exchanges and marking to market [closed]

When a futures exchange marks to the market, does it "help" the losing side or winning side. According to my knowledge, it makes the losing side lose even more by deducting from their margin account? ...
1
vote
1answer
107 views

Upper bound option price in volatility dimension

All, I have a theoretical question about the value of an option when spot price goes to infinity as a function of volatility going to infinity. I know that for a call option: The option value ...
2
votes
1answer
54 views

Optimal number of nodes for binomial lattice?

Let's suppose one is valuing a Euro call on a ZCB in a Black-Derman-Toy lattice. How many nodes/levels of discretization are optimal? Obviously too many creates computational issues and too few ...
2
votes
2answers
261 views

Collateralized / uncollateralized swap

Is a fully collateralized interest rate swap considered free of counterparty credit risk? Or close to risk free? Therefore discounted by the rate that best proxies the risk-free rate (which is the OIS-...
1
vote
1answer
101 views

Lattice pricing of derivatives under multi curve framework (OIS and LIBOR)

My goal is to price various derivatives resetting to 1M and 3M LIBOR via using a lattice. I have calculated an OIS curve for discounting and adjusted 1M and 3M LIBOR forward curves to be consistent ...
2
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0answers
173 views

OTC derivatives trade life cycle

Can someone please walk through a typical OTC derivative trade life cycle? Or could you please provide a good source on that topic? ( I mean things like negotiation - trade execution - trade capture, ...
0
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0answers
451 views

Cashless Exercise of Warrants

This is the formula for a Cashless Exercise of Warrants: X(A-B)/A = Y Where: Y = the number of shares received X = the number of shares purchasable A = price of the stock B = exercise price ...
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0answers
85 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 ...
3
votes
1answer
330 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 ...
3
votes
0answers
66 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 ...
4
votes
2answers
228 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 ...
2
votes
2answers
673 views

Different ways to express a 2s10s steepener?

Some off the top of my head 2s10s cash steepener, however this ages into a 1s9s over time 2s10s swap steepener, better/cleaner way? Are there other ways to express this curve strategy? Would you do ...
2
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0answers
333 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 ...
0
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0answers
34 views

Are there software to compute Initial Margin and MVA and other xVAs?

I have been looking into Matlab, R, Python, but couldn't find any toolbox for computing IM, MVA, xVA for OTC derivatives... Could anybody please point me to some software which can compute these ...
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2answers
39 views

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 ...
1
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1answer
112 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 ...
0
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1answer
89 views

Black 1976 caplet value

I've seen from two sources different formulas for the caplet value (Black 1976): $$Caplet_1 = N\cdot DiscountFactor_{0,k}\cdot yrFrcn_{k,k+1}\cdot [F_{k,k+1}\cdot N(d_1) - R_k\cdot N(d_2)]$$ $$ ...
1
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1answer
300 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 ...
0
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0answers
46 views

Compound option on basket of swaptions

Consider $n$ European Swaptions $S^n$ with exercise dates $T_1 < \dots T_n$. These Swaptions can have different parameters: in particular different strikes, different interest rates, different ...
0
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1answer
411 views

How to use USD OIS discounting for local currency uncollateralised swaps?

I am wanting to do MTM valuations of uncollateralised swaps as our banks have switched to using the USD OIS curve for their discounting (assuming no xVA adjustments). None of the cashflows we are ...
5
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2answers
159 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 ...
0
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1answer
110 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. ...
0
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0answers
40 views

Near-the-money options' range

I basically have one year (2016) of data of vanilla options written on SPX. I was trying to isolate the ATM options, but it is hard to have derivatives having exactly K = S in a given day. For that ...
1
vote
1answer
367 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 ...
1
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1answer
267 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 $...
4
votes
1answer
113 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-...
1
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2answers
1k 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?
1
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1answer
178 views

Quantlib: Getting error trying to price a Swap

I have bootstrapped my curve based on end-of-day data for 24th Nov, 2017 I am then using that to price a off-market swap as below: ...