Formula omitted]-constrained implied transition densities

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This paper presents a practical method of constructing an implied price surface and, more importantly, risk-neutral transition density functions from market option price data, which is the crucial building block of the local volatility surface. We preprocess the market data using the thin plate splines (TPS) in terms of the implied variances, which are the implied volatilities squares times the time to maturities. After prepossessing the market data, we build an implied price surface: cubic spline option price curves that satisfy no-arbitrage conditions. Furthermore, we extract the risk-neutral transition density functions with no extra cost. The extracted risk-neutral transition density functions accurately recover the market option prices.