Questions tagged [derivatives]

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

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1answer
36 views

Does a barrier breach in a geared put structured note result in greater losses for the investor vs a plain knock in barrier?

I understand how knock in barriers work. But what do geared put in a structured note mean? My understanding is in a geared put vs a regular knock in barrier, the loss for the investor is higher if the ...
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45 views

advantage of changing measure

I consider $$Z_n(k):= \exp\{c S^*_n- f(-c)n\}$$ with $f(k):=\log E(e^{kS_1})$ , $S_i=z+i-\sum\limits_{j=1}^iY_j$, $(Y_j)_j$ are i.i.d, $Y_j \in \mathbb{N}_0, z \geq 0$ and $S^*_i:=-S_i$ Define Esscher ...
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What does hedging a structured note mean? Whom does it benefit? [closed]

I am learning to create structured notes for clients. For a reverse convertible note with a basket of underlying equities,providing a guaranteed coupon and having a European knock-in barrier, the ...
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1answer
118 views

How are leveraged futures paid out if they are zero sum?

Alice buys 10 contracts from Bob at 100x leverage and a total cost of £100 - Bob's order was also at 100x leverage. Bob is 10 contracts short and Alice is 10 contracts long. Both have a margin ...
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1answer
239 views

Impact on DV01 of cbot bond futures by changing coupon from 6% to 4%

CBOT has been asking customers lately what their thoughts would be on coupon change from 6% to 4% on all bond futures. I believe the last time this was done was in 2000 where the coupon was changed ...
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2answers
276 views

Option on an Option

What is the value of the contract (to be paid at current time $t_0$) that gives one the right (but not obligation) to buy a Vanilla Call option (with certain strike K) at a pre-determined price $p$ at ...
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1answer
53 views

Why does an autocall on a linear payoff have vega?

Consider a (stochastic) linear index, say $I(t)$, in that it grows at the risk free rate (with some volatility of course). There exists a maturity date $T$ on which I receive $I(T)$; however there is ...
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29 views

Why does an interest rate derivative being in- or out-of-the-money influence the optionality of a multi-currency CSA?

Background Consider a derivative contract with multiple cash CSAs, with the ability of the counterparty posting the collateral to switch to the cheapest-to-deliver (CTD) CSA. Of the possible paths of ...
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4answers
204 views

What book(s) would you recommend for structuring and pricing Exotic Products?

I've been looking for good books on structuring equity derivatives (Principal Protected Notes, Autocalls, Lookbacks, Reverse Convertibles etc). I only found ones that discuss mainly the theoretical ...
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223 views

Pricing Swaption Analytically using Libor Market Model

I was asked the following question in a recent interview: "(i) Express a forward swap rate in terms of forward Libor rates. (ii) Apply Ito's lemma to this expression to derive the process for the ...
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How to calculate reissue price for structured product?

There is a principal structured product which tracks gold prices capped at 12% and 145% Participation. So to achieve this I have kept some amount in Fixed income and rest is used to buy bull call ...
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82 views

Cox-Ingersoll-Ross: Monte Carlo Simulation

I am trying to build a Monte Carlo simulation in Excel (yes, far from optimal) for valuation of a callable bond. I have some experience with MC simulation on path dependent derivatives with stocks as ...
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1answer
83 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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64 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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48 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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27 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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76 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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36 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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4answers
418 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
194 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
115 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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54 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 ...
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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 ...
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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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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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1answer
140 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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49 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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2answers
86 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)...
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43 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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1answer
59 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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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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1answer
122 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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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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1answer
89 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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2answers
227 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 ...
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528 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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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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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 ...
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62 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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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
106 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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1answer
65 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
91 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 ...
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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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1answer
109 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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163 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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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
43 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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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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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 ...

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