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Partially convertible economies face a market-design problem: trade integration, cross-border investment, and domestic balance-sheet exposure increase the demand for currency hedging before full financial integration is complete. China adopted a distinctive architecture for this problem by fostering a deliverable offshore Renminbi market (CNH) alongside the segmented onshore market (CNY), rather than relying only on …
I show that house prices can be modeled using machine learning (kNN and tree-bagging) and a small dataset composed of macro-economic factors (MEF), including an inflation metric (CPI), US treasury rates (10-yr), Gross Domestic Product (GDP), and portfolio size of central banks (ECB, FED). This set of parameters covers all the parties involved in a transaction (buyer, seller, and financing facility) while ignoring the…
We describe a model for evolving commodity forward prices that incorporates three important dynamics which appear in many commodity markets: mean reversion in spot prices and the resulting Samuelson effect on volatility term structure, decorrelation of moves in different points on the forward curve, and implied volatility skew and smile. This model is a "forward curve model" - it describes the stochastic evolution of…
This paper characterizes all continuous price processes that are consistent with current option prices. This extends Derman and Kani (1994) , Dupire (1994 , 1997 ), and Rubinstein (1994) , who only consider processes with deterministic volatility. Our characterization implies a volatility forecast that does not require a specific model, only current option prices. We show how arbitrary volatility processes can be adj…
This article introduces the concept of a statistical arbitrage opportunity (SAO). In a finite-horizon economy, a SAO is a zero-cost trading strategy for which (i) the expected payoff is positive, and (ii) the conditional expected payoff in each final state of the economy is nonnegative. Unlike a pure arbitrage opportunity, a SAO can have negative payoffs provided that the average payoff in each final state is nonnega…
In this paper, we present a numerical method for option pricing and the computation of Greeks under stochastic volatility Bachelier-type models, based on elementary linear algebra. The method allows option prices and Greeks to be computed for infinitely many strikes (within a range of convergence) by evaluating only a finite number of expectations, independent of the number of strikes. For the SABR model, we derive a…
It is well-known that, in the Bachelier model, when asset prices and volatilities are uncorrelated, the implied volatility coincides with the fair value of the volatility swap. In this paper, via classical Itô calculus and Taylor expansions, we write the price for out-of-the-money (OTM) and in-the-money (ITM) options as an expansion with respect to the moneyness, where the coefficients are related to the negative (no…
This paper derives the expressions of correlations between prices of two assets, returns of two assets, and price-return correlations of two assets that depend on statistical moments and correlations of the current values, past values, and volumes of their market trades. The usual frequency-based expressions of correlations of time series of prices and returns describe a partial case of our model when all trade volum…
Time series forecasting is a key tool in financial markets, helping to predict asset prices and guide investment decisions. In highly volatile markets, such as cryptocurrencies like Bitcoin (BTC) and Ethereum (ETH), forecasting becomes more difficult due to extreme price fluctuations driven by market sentiment, technological changes, and regulatory shifts. Traditionally, forecasting relied on statistical methods, but…
Shadow prices simplify the derivation of optimal trading strategies in markets with transaction costs by transferring optimization into a more tractable, frictionless market. This paper establishes that a naïve shadow price Ansatz for maximizing long term returns given average volatility yields a strategy that is, for small bid-ask-spreads, asymptotically optimal at third order. Considering the second-order impact of…
It has been long that literature in financial academics focuses mainly on price and return but much less on trading volume. In the past twenty years, it has already linked both price and trading volume to economic fundamentals, and explored the behavioral implications of trading volume such as investor's attitude toward risks, overconfidence, disagreement, and attention etc. However, what is surprising is how little …
We show that an estimate by de la Peña, Ibragimov and Jordan for $\mathbb{E}(X-c)^+$, with $c$ a constant and $X$ a random variable of which the mean, the variance, and $\mathbb{P}(X \leq c)$ are known, implies an estimate by Scarf on the infimum of $\mathbb{E}(X \wedge c)$ over the set of positive random variables $X$ with fixed mean and variance. This also shows, as a consequence, that the former estimate implies a…
The rapid rise of cryptocurrency prices led to concerns (e.g. the Financial Stability Board) that this wealth accumulation could detrimentally spill over into other parts of the economy, but evidence is limited. We exploit the tendency for metaverses to issue their own cryptocurrencies along with non-fungible tokens (NFTs) representing virtual real estate ownership (LAND) to provide evidence of the wealth effect. Cry…
Janardan (1980) introduces a class of offspring distributions that sandwich between Bernoulli and Poisson. This paper extends the Janardan Galton Watson (JGW) branching process as a model of stock prices. In this article, the return value over time t depends on the initial close price, which shows the number of offspring, has a role in the expectation of return and probability of extinction after the passage at time …
In this paper, we investigate the impact of mortgage rates on home prices, and how the impact may be used to help property purchase discussions at individual buyer level and to adjust home price indices across time. A mortgage-rate-adjusted "effective price" is derived to measure near term property price in the presence of (expected) mortgage rate changes. A price-mortgage rate neutrality line is then constructed bas…
The aim of the present work is analysing and understanding the dynamics of the prices of companies, depending on whether they are included or excluded from the STOXX Europe 600 Index. For this reason, data regarding the companies of the Index in question was collected and analysed also through the use of logit models and neural networks in order to find the independent variables that affect the changes in prices and …
We present a method for the arbitrage-free interpolation of plain-vanilla option prices and implied volatilities, which is based on a system of integral equations that relates terminal density and option prices. Using a discretization of the terminal density, we write these integral equations as a system of linear equations. We show that the kernel matrix of this system is in general ill-conditioned, so that it can n…
We analyze the interaction between stock prices of big companies in the USA and Germany using Granger Causality. We claim that the increase in pair-wise Granger causality interaction between prices in the times of crisis is the consequence of simultaneous response of the markets to the outside events or external stimulus that is considered as a common driver to all the stocks, not a result of real causal predictabili…
Gamma Hedging — Delta adjustments by dealers that can accelerate trends or pin prices near strikes.
A bear steepener is a curve move where long yields rise more than front yields (or fronts fall less) as the market prices more term premium, more deficit, or less faith in long-run restraint — and duration loses.
Bidless means there is no meaningful posted or workable bid — you can sell only by walking the stairs or waiting, which is how fire sales become prices.
The quantity theory is MV = PY: money times velocity equals nominal income. In the strong form, a one-off money increase raises prices one-for-one if V and Y are stable.
CPI is a fixed-basket consumer-price index — the headline inflation print that sets TIPS, Social Security, and a lot of politics.
Deflation is a sustained fall in the general price level — often a demand or debt-deleveraging story, dangerous when nominal debt is high.
Disinflation is a falling inflation rate while prices still rise — the 2023 word, not deflation.
Inflation is a sustained rise in the general price level — a decline in purchasing power, not a one-off relative-price shock.
PPI measures prices from the seller’s side of the pipeline — an upstream inflation print that may or may not pass through to CPI.
The Great Depression was a multi-year collapse of output, prices, and banks after the 1929 crash, amplified by the gold standard, Fed errors, and a wave of bank failures — the defining 20th-century crisis.
The Hunt brothers’ 1979–80 silver corner drove prices from single digits toward $50 before exchange rule changes and a margin spiral crushed the trade on Silver Thursday.
The 1973–74 OPEC embargo quadrupled oil prices, fused inflation with a growth shock (stagflation), and ended the last illusions of the post-war energy-cheap regime.
A callable bond lets the issuer redeem early at a schedule of prices — you sold a call to the issuer and should be paid for it.
The Fed’s dual mandate is maximum employment and stable prices — two goals that agree in a demand shock and fight in a supply shock.
A risk-neutral (equivalent martingale) measure is a probability reweighting that makes discounted asset prices martingales — prices are then discounted expected payoffs under that measure, not under the real-world P.
A circuit breaker is an exchange halt when prices move too far too fast — a pause so the book can rebuild, not a valuation.
A limit order book is the visible (and sometimes hidden) queue of bids and offers at discrete prices that constitutes the tradable supply and demand of a continuous electronic market.
A market order is an instruction to buy or sell now at the best available prices — certainty of fill, uncertainty of price.
EMH says prices reflect available information so that you cannot systematically earn risk-adjusted profits from that information — a benchmark, not a religion.
A bear steepener is a curve move where long yields rise more than front yields (or fronts fall less) as the market prices more term premium, more deficit, or less faith in long-run restraint — and duration loses.
Bidless means there is no meaningful posted or workable bid — you can sell only by walking the stairs or waiting, which is how fire sales become prices.
A callable bond lets the issuer redeem early at a schedule of prices — you sold a call to the issuer and should be paid for it.
A circuit breaker is an exchange halt when prices move too far too fast — a pause so the book can rebuild, not a valuation.
Disinflation is a falling inflation rate while prices still rise — the 2023 word, not deflation.
The Fed’s dual mandate is maximum employment and stable prices — two goals that agree in a demand shock and fight in a supply shock.
EMH says prices reflect available information so that you cannot systematically earn risk-adjusted profits from that information — a benchmark, not a religion.
Gamma Hedging — Delta adjustments by dealers that can accelerate trends or pin prices near strikes.
The Great Depression was a multi-year collapse of output, prices, and banks after the 1929 crash, amplified by the gold standard, Fed errors, and a wave of bank failures — the defining 20th-century crisis.
The Hunt brothers’ 1979–80 silver corner drove prices from single digits toward $50 before exchange rule changes and a margin spiral crushed the trade on Silver Thursday.
A limit order book is the visible (and sometimes hidden) queue of bids and offers at discrete prices that constitutes the tradable supply and demand of a continuous electronic market.
A market order is an instruction to buy or sell now at the best available prices — certainty of fill, uncertainty of price.
The 1973–74 OPEC embargo quadrupled oil prices, fused inflation with a growth shock (stagflation), and ended the last illusions of the post-war energy-cheap regime.
PPI measures prices from the seller’s side of the pipeline — an upstream inflation print that may or may not pass through to CPI.
The quantity theory is MV = PY: money times velocity equals nominal income. In the strong form, a one-off money increase raises prices one-for-one if V and Y are stable.
A risk-neutral (equivalent martingale) measure is a probability reweighting that makes discounted asset prices martingales — prices are then discounted expected payoffs under that measure, not under the real-world P.