Questions tagged [pricing]

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14
votes
3answers
5k views

What is the Risk Neutral Measure?

What is the Risk Neutral Measure? I don't believe this has been answered on the internet well and with all the parts connecting. So: What is the risk neutral measure/pricing? Why do we need it? How ...
11
votes
2answers
3k views

How to derive the price of a square-or-nothing call option?

At maturity $T$, the holder of a "square-or-nothing" call option written on an underlying $S_t$ receives a payoff of the form $$ \phi(S_T) = \frac{S_T^2}{K} \pmb{1}_{\{S_T \geq K\}} = \begin{cases}\...
2
votes
1answer
338 views

Valuation of Corridor Variance Swaps

Given that the payout of the Corridor Variance Swap (CVS) is $V \left(\frac{\sum_{n=0}^{N}I}{T_2 - T_0} (\sigma^2 - K^2) \right)$, where $\sigma^2$ is the realized variance within the pre-specified ...
5
votes
1answer
245 views

Change of measure's impact on parameter value

This is a follow-up question on Price of a prepayment-based claim. Consider a zero-coupon bond of maturity $T$ with price $P_0$ for which the borrower can reimburse the principal $N$ at any time $\...
23
votes
2answers
14k views

Cross Currency Swap Pricing in nowadays environment

Multicurve setting has now become the new paradigm for vanilla swap valuation. For the record I give here (without getting into too much details) the methodoloy for pricing Euribor3M swaps in this ...
8
votes
1answer
2k views

Arbitragefree Pricing: Q vs. P

I read that the Fundamental Theorem of Asset Pricing states, that a market is arbitrage-free if and only if there exists an equivalent martingale measure Q, under which the discounted asset price ...
5
votes
2answers
8k views

How to get real-time data for Fama-French model?

For Fama-French model we need SMB (small[market cap] minus big) and HML (high[book-to-market-ratio] minis low). I want to ...
0
votes
1answer
431 views

What is the value/price of a bond paying floating rate

I am going through J.C.Hull for swaps. Where he says we can value a swap using bonds. Let $B_{fl}$: value of floating rate bond, $L$ notional principal. Why is $B_{fl} = L$ just after a payment ? What ...
18
votes
1answer
15k views

What is the reason for the convexity adjustment when pricing a constant maturity swap (CMS)?

I'm trying to wrap my head around pricing a Constant Maturity Swap (CMS). Let's imagine the following deal: 6m LIBOR in one direction, 10y swap rate in the other. The discount curve is derived from ...
23
votes
2answers
3k views

Which interest rate model for which product

Given the multitude of existing interest rate models (ranging from simple to very complex) it would be interesting to know when the additional complexity actually makes sense. The models I have in ...
11
votes
1answer
2k views

Price functions based on order book events

Assume some equity traded on a given exchange based on an electronic limit open-order book $B$ that makes sequential updates as a function of time $t$. What are "natural" or common price functions $P: ...
14
votes
3answers
3k views

Implementing a Fast Fourier Transform for Option Pricing

So, I'm in need of some tips regarding a small project I'm doing. My goal is an implementation of a Fast Fourier Transform algorithm (FFT) which can be applied to the pricing of options. First ...
10
votes
2answers
429 views

Differences between main classes of interest pricing derivatives models

There seems to be 3 main classes of interest rate pricing models: 1) Short rate models, 2) Heath Jarrow models and 3) Libor Market Model. My book doesnt seem to explain why we need all these different ...
6
votes
2answers
314 views

Can the concept of negative probabilities be used to price a call option?

Edit: I'm a dumbass. The thing below is supposed to be just the motivation of asking. I want to ask for below and in general, hehe. Assume that we have a general one-period market model consisting of ...
11
votes
4answers
7k views

What is the importance of alpha, beta, rho in the SABR volatility model?

I just read that SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands for "stochastic alpha, beta, rho", referring to the ...
13
votes
2answers
2k views

For which instruments performs SABR/LMM better than LMM?

For which class of instruments the SABR/LIBOR Market Model does perform better than the classical LIBOR Market Model? The LIBOR Market Model The LIBOR Market Model — also known as Brace, Gatarek, ...
8
votes
1answer
237 views

FTAP a-la Harrison, Kreps and Pliska

I was reading the papers co-authored by Harrison, Kreps and Pliska, that initiated the formal research on the connection between pricing, martingale measures, arbitrage and completeness. I have some ...
7
votes
1answer
21k views

The difference between Close price and Settelment Price for future contracts

What is the difference between Close price and Settlement Price for future contracts? Is there a defined rule for evaluating the settlement price or different rules are applied for each instrument/...
3
votes
1answer
152 views

Pricing homogeneous Basket Default Swap

Consider a basket with $K=10$ names. Default times of the names, $\tau_k$, are i.i.d. random variables with distribution $P(\tau_k \leq t) = 1 - e^{-\lambda t}$. Suppose that each name in the basket ...
5
votes
2answers
7k views

How to derive Black's formula for the valuation of an option on a future?

I've got a question about 1976 Black Model and Bachelier model. I know that a geometric brownian motion in the P measure $dS_{t}=\mu S_{t}dt+\sigma S_{t} dW_{t}^{P}$ for a stock price $S_{t}$ leads (...
4
votes
4answers
7k views

What is the Most Efficient Way to Calculate the Internal Rate of Return IRR?

I have built a program that prices financial assets and it does this in part by calculating the IRR. The problem is that it does not run as quickly as I would like it to. I currently use the Newton-...
4
votes
1answer
862 views

Pricing interest rate swap in Ho Lee model

In Ho Lee model, assuming risk neutral probability is not exactly 0.5, would a change in the volatility of short-term rate affect the price of an interest rate swap? My intuition tells me no as ...
1
vote
1answer
85 views

Copula analytic formula for $max(S_T^1 - K, 0) 1_{\{L<S_T^2<U\}}$

Consider the payoff function $$ V_T = max(S_T^1 - K, 0) 1_{\{L<S_T^2<U\}} = (S_T^1 - K)1_{\{S_T^1 > K\}}1_{\{L<S_T^2<U\}}$$ where $S_T^1$ and $S_T^2$ are two GBM distributed stocks with ...
0
votes
1answer
601 views

Do FRN's *always* trade on par on reset days, regardless if the issuer's credit quality has changed?

I keep reading that floating rate notes trade on par on coupon reset days. Is this always true, regardless of changes in the issuer's credit quality since the FRN was issued? It seems probably ...
3
votes
1answer
59 views

Price of a prepayment-based claim

I am trying to determine the pricing formula for a given claim inspired in prepayment obligations backed by mortgage portfolios $-$ I believe these were popular in the eighties. The product ...
2
votes
3answers
4k views

FX Delta Conventions

I'm currently reading Iain Clark's book Foreign Exchange Option Pricing and I got stuck at one sentence in the beginning of Section 3.3 that I feel is important to understand. He writes: FX ...
2
votes
1answer
344 views

What is the filtration described?

What is the filtration $(\mathfrak{F}_t)$ encircled below? Is it $(\mathfrak{F}_t) = (\sigma(W_t)) = (\sigma(\tilde{W_t})), t \in [0,T]$? Or is it $(\mathfrak{F}_t) = (\sigma(\hat{W_t})), t \in [0,T]...
2
votes
1answer
263 views

How do traders come up with prices for derivatives?

As a follow up to a recent question on why market prices and model prices can sometimes differ substantially, this resulted in a new question. How do traders come up with prices? Example: Let's say ...
1
vote
1answer
164 views

Quantlib: How do I price a bond after having built a term structure

I below are my codes using QuantLib to build a term structure What I would like to do is use that to price any hypothetical bond lets say startdate : 8 Feb 2016 end date : 8 Feb 2021 coupons : 10% ...