Questions tagged [derivatives]

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

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3
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0answers
141 views

Estimate market price of risk $\lambda_t$

The pricing of derivatives in a risk-neutral framework often requires the input of an unobservable market price of risk. Let us assume that we observe two macroeconomic factors in the state vector $...
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1answer
72 views

PnL due to model recalibration and its relationship with hedging error

Consider the case where at t=0, I calibrate my model to the market, but at t=1 my model is no longer able to recover the price in the market, so it needs recalibration. Say I have delta hedged my ...
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61 views

Can you predict MTM gain or losses on future contract?

I am working on a structured product where I am investing some percentage of invested amount in futures contract. I have created a bull put strategy and I will calculate the delta positions of that ...
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0answers
41 views

Estimate of basket volatility

We are looking for a simple way to calculate an approximation of the basket volatility for a set of baskets so that we can estimate which basket might produce the highest coupon in a standard ...
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0answers
25 views

Are there noticeable jumps in index options price due to systematic hedging of structured products close to big expiry dates?

I am looking at investigating factors that will cause jumps in index options prices close to big expiries in the name. I imagine systematic rebalancing of structured products will have a large impact ...
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4answers
372 views

Find a formula for the price of a derivative paying $\max(S_T(S_T-K),0)$

Develop a formula for the price of a derivative paying $$\max(S_T(S_T-K))$$ in the Black Scholes model. Apparently the trick to this question is to compute the expectation under the stock measure. So,...
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1answer
69 views

How can we unwind a Index ( SPX ) Variance swap?

Client A comes to dealer to trade variance notional $1m at T=0. The trade is executed with dealer short volatility with strike of 20. term Payoff of dealer = notional*( Stike^2 - realized vol^2 ) now ...
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1answer
32 views

The relationship between volatility of underlying asset, leverage and the volatility of the derivative

If I want to lower the risk of the portfolio then the trivial thing to do is change from higher volatility to lower for a better Sharpe ratio. It already lists the volatility for the stocks but the ...
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6answers
402 views

What is the benefit of holding a short option?

I am new to corporate finance and I ask myself why an investor is interested in being short an option? He can only can win a premium but he can lose much more. I understand with being a short, I cap ...
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1answer
177 views

Software implementation for valuation of exotic options

I am looking for some software implementation of pricing Average Price Call option (APO) mostly Python (or any other package.) Exercise style is ...
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1answer
52 views

Convexity of a rates Bermudan w.r.t strike

Recently there was a nice question asked on convexity of American put w.r.t strike: Convexity of an American put option Does the same hold for a Bermudan option in rates, where they underlyings are ...
2
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1answer
103 views

What kind of entities use exotic derivatives, and do they serve any purpose other than hedging risk?

I work in a sell-side bank in derivatives modeling. My work involves modeling and pricing of exotic derivatives and I often wonder who are the buyers of these products. From my research, I found that ...
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0answers
29 views

Does equity premium puzzle affect option-implied RWDs using Arrow-Debreu equilibrium?

I am researching and learning about option-implied RNDs (risk neutral densities) and transformation to RWDs (risk world densities) using expected utility theory to compute risk aversion values. This ...
4
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1answer
115 views

Understanding the notion of future options

I am currently studying different types of option-related derivatives and I am quite confused about the notion of “futures options”. My textbook says that A futures option is the right, but not ...
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0answers
53 views

What are the most difficult/computationally expensive/infeasible derivatives to price?

I'm not sure if this question has a concrete answer or if it's more of a fun game, but I suppose the question that does have a concrete answer is what's the most difficult instrument to value that has ...
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29 views

Black model with negative strike price

Whats the issue if we try to price a swaption with a negative strike using Black model?
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2answers
81 views

lead lag relationship among futures, options and stock prices

I have the data of past 10 years of NIFTY (the National Stock Exchange of India) stock, futures and options and I want to show the lead-lag relationship (which reacts first, futures, options or stocks)...
2
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1answer
101 views

Bermudan option exercise probability when rates rise

I am looking for an explanation of what happens to the Bermudan exercise probability (i.e. does probability of early exercise go higher if rates rise or lower) w.r.t rates. This is of course with ...
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1answer
186 views

What happens to both sides of an inflation swap agreement if there is deflation?

If there is deflation does the Inflation receiver not only pay the fixed leg but also receives a reduced CPI? I.e. does he lose twice?
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0answers
48 views

Options pricing model inversion

He cited about Roll's compound formula for finding the lead-lag effects between stocks and options. I have a similar data for National Stock Exchange's Index, NIFTY but it's daily, not intra-day. I ...
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4answers
358 views

Using a Constant as a Numeraire

Please provide steps to justify the below. 1) Can we use a constant as a numeraire? Related Question: Scaling Stock Price and Strike etc. by a Constant The rest of standard Geometric Brownian ...
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0answers
38 views

How do I calculate FX forward hedge ratio?

Suppose I have a USD holding of 1,000,000 in my portfolio and I want to convert it into EUR in a month's time. I enter into a FX forward contract of the same amount USD 1,000,000, meaning that I have ...
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4answers
16k views

What is a Constant Maturity Swap (CMS) rate?

I have been searching in books and on the internet for a basic definition and explanation of CMS rates, but I cannot find anything clear and simple. Can you explain (maybe with an example) what a CMS ...
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1answer
50 views

Is the forward price equal to the future price?

If $f^{T_1}(t)$ is the price of a forward and $F^{T_1}(t)$ is the price of a future on some stock, both maturing at date $T_1$ and with the assumptions: no dividend constant interest rates no ...
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1answer
71 views

What to do if certain parameters are not market observable?

Lets say I have no clue on correlation between 2 equities in the market (i.e. i don't have an observable market price). What is the best way to go about marking this correlation for lets say the best ...
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0answers
24 views

Local v/s global calibration for a Bermudan Option (calibrate co-terminals vs entire matrix)

I am quite new to rates modeling and I have a question on the pros and cons of calibrating to larger set of vanilla instruments v/s calibrating to an exotic's 'natural' hedges. For example, I could ...
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5answers
503 views

bank issuing structured products

"The investment banks supplying structured products were effectively buying options from investors" How to understand this quote from this source? I would think the investors are usually had (long) ...
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1answer
119 views

Do different prices under different models admit arbitrage?

There are many models for interest rate. If two people use two different models to price the same interest rate derivative, and come to two different prices, doesn't that admit an arbitrage? How ...
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1answer
68 views

Extensive list of financial derivatives and what method is used to value them

What I'm imagining is a long list of different types of financial instruments traded on the market along with the model(s) that is industry standard for valuing it. Something like: European equity ...
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0answers
45 views

Issue with solving American call option questions

Here are the questions: I tried using DerivaGem, but I am not sure that I got the right result. Here are my attempts at solving the questions: a) Upper and lower bound: Is it correct? Not sure ...
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2answers
151 views

What does the word “affine” mean in affine term structure models?

I am new to the field of Mathematical Finance and wanted to get an idea on the intuitive, physical and mathematical meaning of the term "affine" in Affine term structure models. Any literature ...
2
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1answer
307 views

Exercise Probabilities Vanilla Cap/Floor

When looking at the discounted pay-off formulas of a vanilla caplet and a vanilla floorlet $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_k-r_{cap},0)$ $\frac{\Delta\tau}{1+r_k\Delta\tau}\max(r_{floor}-...
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1answer
52 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 ...
2
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1answer
81 views

Callable Total Return Swap pricing

I need to price a callable Equity Return Swap by Accrual. ERS has property callable T+1 and I don't get it. Does it mean that when a call happen we fix a price that and pay Accrual the next day? Could ...
2
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3answers
244 views

How do market makers chose the size that they quote?

A typical quote in the derivatives market may be 2.00 bid at 2.50 ask with a size of say 100x100. How do practitioners go about choosing the size of the market (how many contracts) to quote? It seems ...
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0answers
19 views

Contingent Claim Bounds

In my course on discrete-time finance we derived the following equality for a lower bound for the value of a not necessarily replicable contingent claim $D$. Here we are looking at a single period ...
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0answers
61 views

Types of financial derivatives

I am looking for an explanation for different types/grades of derivatives. For example we have various asset classes: equities FX (currency) derivatives, etc. Or different types of secured debts, ...
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0answers
39 views

Is Vega hedging a complex derivative self financing?

Let's consider an incomplete market where I am pricing a complex derivative (Say a Bermudan). I hedge vega by a vanilla option(S). Let's say at t=1 I want to re-hedge. However, I have no guarantee ...
6
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2answers
128 views

Radon Nikodym derivative when changing numeraires

I note from Wikipedia that if $Q$ and $Q^N$ are two measures corresponding to numeraires $M$ and $N$, then the Radon Nikodym derivative is given by: $$\frac{dQ^N}{dQ} = \frac{M(0)}{M(T)}\frac{N(T)}{N(...
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0answers
33 views

Fourier transform of price function

If the expiry value is given by $f(x,T) = e^{-c x}$ for $x \ge a$ and 0 otherwise and c is a +ve constant, prove that in the Fourier domain: $$ (c + j \omega) F(\omega, 0) = e^{-rT} e^{-a(c+j\omega)}...
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1answer
1k views

Stochastic modelling of derivatives on dividends

I consider pricing and risk analysis of derivatives on dividends of the members of equity indices (such as Dow Jones EuroStoxx). There are options but I focus on futures. What are common stochastic ...
0
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1answer
47 views

Equal prices for call and put options with symmetric strikes around contemporaneous price?

Shouldn't (according to the Black-Scholes model) the price of a call option with a strike of an arbitrary amount away from the current asset's price, be equal to the price of a put option with the ...
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1answer
92 views

Calculate Third Order Greeks Options

Hope you're doing great! I'm struggling to develop the code for the Third Order Greeks. In all places I have searched, the development is missing. For example: But I don't know how to develop it, ...
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0answers
14 views

Balance sheet items which might show exposure to hedging or the prevalence of forward contracts

I do have a panel data set on North American companies from Compustat covering balance sheet and income information. I am wondering if there is a possibility to use a balance sheet variable as an ...
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0answers
29 views

Models for derivative portfolio composition

I focus on interest rate derivatives. I am looking for theoretical references which would model how financial institutions optimally choose among the different types of existing instruments (options, ...
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1answer
33 views

Synthetic FRAs using Eurodollar futures

In order to create a synthetic FRA position of 30-day FRA on 90-day LIBOR, the diagram below shows that we can enter into positions by going long a 120-day Eurodollar contract and short a 30-day ...
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1answer
34 views

The NA price of a caplet with payoff

Prove the following statement: The NA price of a caplet with payoff $$\delta \cdot (L(T;T,T+\delta)-k)^{+} $$ at time $T+\delta$ equals the NA price of a put option with the payoff $$(1+\delta \cdot k)...
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2answers
229 views

When would open interest equal trading volume?

I know the difference between open interest and trading volume. Open interest is the number of contracts, long or short, outstanding. Trading volume is the number of contracts traded in a day. ...
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0answers
25 views

Bond CSA hedging risk

If I have a CSA that contains say GBP Gilts and GBP cash, how do i hedge the risk that the gilt funding cost goes up. Lets say my portfolio is > 10 years. Let's assume I have a discount curve that ...
4
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2answers
182 views

Why do some principal-protected notes reset the gains to zero?

I was looking through the principal-protected notes issued by Lehman Brothers. One of them was the "100% Principal Protection Absolute Return Barrier Notes Linked to the S&P 500 Index". The ...

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