No Arbitrage SVI

Smiles in delta

“…As shown in section 2.3 of [9], the condition of vanishing Call prices for increasing strikes is not necessary. Such condition is one-to-one with the behavior of the function d 1 at ∞.…”

On the harmonic mean representation of the implied volatility

“…The strict monotonicity of the maps f 0 and f 1 can be exploited to rigorously justify some remarkable model-free pricing formulas for European claims such as the log-contract, see [7,11,8] and section 5.1 below, and can also be used as a partial characterization of the static no-arbitrage condition on v, see Remark 2.5 below and the work carried out in [18].…”

“…In Figure 1, as an illustration we plot two examples of implied volatility smiles and their related functions h. The SVI parameterization, introduced by Gatheral in 2004 [13], is defined by w This set of parameters generate an arbitrage-free smile, as it can be checked using the procedure described in [18]. Right: SSVI parameters are θ = 0.25, ρ = 0.7, ϕ = 3.…”

“…Figure 1: Examples of arbitrage-free implied volatilities and their related functions h in Theorem 2.4. Left: SVI parameters are a = 0.04, b = 0.4, ρ = −0.7, m = 0.1, σ = 0.2.This set of parameters generate an arbitrage-free smile, as it can be checked using the procedure described in[18]. Right: SSVI parameters are θ = 0.25, ρ = 0.7, ϕ = 3.…”

No arbitrage global parametrization for the eSSVI volatility surface

“…The Stochastic Volatility Inspired model for the total implied variance proposed by Gatheral at the Global Derivatives conference in Madrid in 2004 [5] fits notably well market data and, even restricting the 5 parameters domain to a Butterfly arbitrage-free domain (as characterized by Martini and Mingone in [10]), the model still guarantees accurate smile fitting. However, conditions for the absence of Calendar spread arbitrage arising when smiles of different maturities are glued into a continuous surface are still not known and this limits the practical applications of this model.…”