Option Valuation in Multivariate SABR Models

We consider the joint dynamic of a basket of n-assets where each asset itself follows a SABR stochastic volatility model. Using the Markovian Projection methodology we approximate a univariate displaced diffusion SABR dynamic for the basket to price caps and floors in closed form. This enables us to consider not only the asset correlation but also the skew, the cross-skew and the decorrelation in our approximation. The latter is not possible in alternative approximations to price e.g. spread options. We illustrate the method by considering the example where the underlyings are two constant maturity swap (CMS) rates. Here we examine the influence of the swaption volatility cube on CMS spread options and compare our approximation formulae to results obtained by Monte Carlo simulation and a copula approach.SABR; CMS spread; displaced diffusion; Markovian projection; GyÄongy Lemma

Essays about Option Valuation under Stochastic Interest Rates

This thesis consists of three essays on the valuation of options under stochastic interest rates. In the first essay we examine multivariate models where the stochastic process of a log-normally distributed underlying depends on the evolution of correlated interest rate processes. There the correlation structure can change by constant factor volatilities, which influences not only the values of financial instruments but also their hedge strategies. In this model class we propose a unified framework for the pricing and hedging of chooser options under stochastic interest rates. Chooser options are exotic derivatives who give the owner the right to enter at their exercise date a call or a put option with the same underlying. The chosen multivariate framework allows to derive closed form solutions of the arbitrage price for different specifications of chooser options such as different strike prices or time to maturities. The second essay deals with the so called convexity correction of swap rates. A convexity correction needs to be computed in the case of constant maturity swaps (CMS) for example. The expectation is taken under a different measure than the assets martingale measure. Then, the expectation is not the forward value but the forward value plus a convexity correction. One approach in the literature suggests, that the convexity correction is the price of a static portfolio of plain-vanilla swaptions. This portfolio approach has the advantage that the volatility cube can be incorporated by using a stochastic or local volatility models, but it is the solution of an integral over an infinite number of strike prices. We propose an algorithm to approximate the replication portfolio with a finite number and therefore a discrete set of strike prices. The accuracy of the method is examined using numerical examples and different valuation models as well as different sets of strike prices. The modeling of multi-asset options within an interest rate model is the topic of the third essay. There, we consider the joint dynamic of a basket of n-assets with the application to CMS spread options in mind. Therefore we use a Swap Market Model (SMM) with deterministic volatility and the SABR model with stochastic volatility. Using the Markovian Projection methodology we approximate multivariate SMM/SABR dynamic with a univariate SMM/SABR dynamic to price caps and floors in closed form. This enables us to consider not only the asset correlation but, in the case of the SABR model, as well the skew, the cross-skew and the decorrelation in our approximation. If for example, spread options are considered the latter is not possible in alternative approximations. We illustrate the method by considering the example where the underlyings are two constant maturity swap rates. There we examine the influence of the swaption volatility cube on CMS spread options and compare our approximation formulae to results obtained by Monte Carlo simulation and a copula approach

IT'S YOUR CHOICE: A UNIFIED APPROACH TO CHOOSER OPTIONS

We propose a unified framework for the pricing and hedging of chooser options on lognormal assets. This includes e.g. exchange or inflation rates under stochastic interest rates or equities under stochastic interest rates and dividend yields. This extends and includes chooser options under deterministic interest rates by a multidimensional model of an international economy with correlated stochastic processes. In this framework we derive closed form solutions of the arbitrage price for different specifications of chooser options. Also different hedge strategies are derived and their properties compared.Option pricing and hedging, interest rate risk, exchange rate risk, change of numeraire

Orthogonal assembly of a designed ankyrin repeat protein-cytotoxin conjugate with a clickable serum albumin module for half-life extension

The generation of drug conjugates for safe and effective tumor targeting requires binding proteins tolerant to functionalization by rational engineering. Here, we show that Designed Ankyrin Repeat Proteins (DARPins), a novel class of binding proteins not derived from antibodies, can be used as building blocks for facile orthogonal assembly of bioconjugates for tumor targeting with tailored properties. DARPin Ec1, which targets the Epithelial Cell Adhesion Molecule (EpCAM), was genetically modified with a C-terminal cysteine for conjugation of the small molecule cytotoxin monomethylauristatin F (MMAF). In addition, it was N-terminally functionalized by metabolic introduction of the non-natural amino acid azidohomoalanine to enable linkage of site-specifically dibenzocyclooctyne-modified mouse serum albumin (MSA) for half-life extension using Cu(I)-free click chemistry. The conjugate MSA-Ec1-MMAF was assembled to obtain high yields of a pure and stable drug conjugate as confirmed by various analytical methods and in functional assays. The orthogonality of the assembly led to a defined reaction product and preserved the functional properties of all modules, including EpCAM-specific binding and internalization, FcRn binding mediated by MSA, and cytotoxic potency. Linkage of MMAF to the DARPin increased receptor-specific uptake of the drug while decreasing nonspecific uptake, and further coupling of the conjugate to MSA enhanced this effect. In mice, albumin conjugation increased the serum half-life from 11 min to 17.4 h, resulting in a more than 22-fold increase in the area-under-the-curve (AUC). Our data demonstrate the promise of the DARPin format for facile modular assembly of drug conjugates with improved pharmacokinetic performance for tumor targeting

Epithelial cell adhesion molecule-targeted drug delivery for cancer therapy

INTRODUCTION: The epithelial cell adhesion molecule (EpCAM) is abundantly expressed in epithelial tumors, on cancer stem cells and circulating tumor cells. Together with its role in oncogenic signaling, this has sparked interest in its potential for tumor targeting with antibodies and drug conjugates for safe and effective cancer therapy. Recent advances in protein engineering, linker design and drug formulations have provided a multitude of EpCAM-targeting anticancer agents, several of them with good perspectives for clinical development. AREAS COVERED: This article reviews the biological, therapeutic and technical aspects of EpCAM-targeted drug delivery for cancer therapy. The authors discuss seminal findings, which distinguish EpCAM as a target with oncogenic function and abundant expression in epithelial tumors. Moreover, recent trends in engineering improved anti-EpCAM antibodies, binding proteins that are not derived from immunoglobulins and drug conjugates derived from them are highlighted and their therapeutic potential based on reported preclinical and clinical data, originality of design and perspectives are critically assessed. EXPERT OPINION: EpCAM has shown promise for safe and efficient targeting of solid tumors using antibodies, alternative binding molecules and novel drug conjugates. Among the myriad of EpCAM-targeting drug delivery systems investigated so far, several could demonstrate therapeutic benefit, other formulations engineered to become tailor-made missiles are on the brink

Increasing the Antitumor Effect of an EpCAM-Targeting Fusion Toxin by Facile Click PEGylation

Fusion toxins used for cancer-related therapy have demonstrated short circulation half-lives, which impairs tumor localization and, hence, efficacy. Here, we demonstrate that the pharmacokinetics of a fusion toxin composed of a designed ankyrin repeat protein (DARPin) and domain I–truncated Pseudomonas Exotoxin A (PE40/ETA″) can be significantly improved by facile bioorthogonal conjugation with a polyethylene glycol (PEG) polymer at a unique position. Fusion of the anti-EpCAM DARPin Ec1 to ETA″ and expression in methionine-auxotrophic E. coli enabled introduction of the nonnatural amino acid azidohomoalanine (Aha) at position 1 for strain-promoted click PEGylation. PEGylated Ec1-ETA″ was characterized by detailed biochemical analysis, and its potential for tumor targeting was assessed using carcinoma cell lines of various histotypes in vitro, and subcutaneous and orthotopic tumor xenografts in vivo. The mild click reaction resulted in a well-defined mono-PEGylated product, which could be readily purified to homogeneity. Despite an increased hydrodynamic radius resulting from the polymer, the fusion toxin demonstrated high EpCAM-binding activity and retained cytotoxicity in the femtomolar range. Pharmacologic analysis in mice unveiled an almost 6-fold increase in the elimination half-life (14 vs. 82 minutes) and a more than 7-fold increase in the area under the curve (AUC) compared with non-PEGylated Ec1-ETA″, which directly translated in increased and longer-lasting effects on established tumor xenografts. Our data underline the great potential of combining the inherent advantages of the DARPin format with bioorthogonal click chemistry to overcome the limitations of engineering fusion toxins with enhanced efficacy for cancer-related therapy

Novel Prodrug-Like Fusion Toxin with Protease-Sensitive Bioorthogonal PEGylation for Tumor Targeting

Highly potent biotoxins like Pseudomonas exotoxin A (ETA) are attractive payloads for tumor targeting. However, despite replacement of the natural cell-binding domain of ETA by tumor-selective antibodies or alternative binding proteins like designed ankyrin repeat proteins (DARPins) the therapeutic window of such fusion toxins is still limited by target-independent cellular uptake, resulting in toxicity in normal tissues. Furthermore, the strong immunogenicity of the bacterial toxin precludes repeated administration in most patients. Site-specific modification to convert ETA into a prodrug-like toxin which is reactivated specifically in the tumor, and at the same time has a longer circulation half-life and is less immunogenic, is therefore appealing. To engineer a prodrug-like fusion toxin consisting of the anti-EpCAM DARPin Ec1 and a domain I-deleted variant of ETA (ETA″), we used strain-promoted azide alkyne cycloaddition for bioorthogonal conjugation of linear or branched polyethylene glycol (PEG) polymers at defined positions within the toxin moiety. Reversibility of the shielding was provided by a designed peptide linker containing the cleavage site for the rhinovirus 3C model protease. We identified two distinct sites, one within the catalytic domain and one close to the C-terminal KDEL sequence of Ec1-ETA″, simultaneous PEGylation of which resulted in up to 1000-fold lower cytotoxicity in EpCAM-positive tumor cells. Importantly, the potency of the fusion toxin was fully restored by proteolytic unveiling. Upon systemic administration in mice, PEGylated Ec1-ETA″ was much better tolerated than Ec1-ETA″; it showed a longer circulation half-life and an almost 10-fold increased area under the curve (AUC). Our strategy of engineering prodrug-like fusion toxins by bioorthogonal veiling opens new possibilities for targeting tumors with more specificity and efficacy

Facile Double-Functionalization of Designed Ankyrin Repeat Proteins using Click and Thiol Chemistries

Click chemistry is a powerful technology for the functionalization of therapeutic proteins with effector moieties, because of its potential for bio-orthogonal, regio-selective, and high-yielding conjugation under mild conditions. Designed Ankyrin Repeat Proteins (DARPins), a novel class of highly stable binding proteins, are particularly well suited for the introduction of clickable methionine surrogates such as azidohomoalanine (Aha) or homopropargylglycine (Hpg), since the DARPin scaffold can be made methionine-free by an M34L mutation in the N-cap which fully maintains the biophysical properties of the protein. A single N-terminal azidohomoalanine, replacing the initiator Met, is incorporated in high yield, and allows preparation of “clickable” DARPins at about 30 mg per liter <i>E. coli</i> culture, fully retaining stability, specificity, and affinity. For a second modification, we introduced a cysteine at the C-terminus. Such DARPins could be conveniently site-specifically linked to two moieties, polyethylene glycol (PEG) to the N-terminus and the fluorophore Alexa488 to the C-terminus. We present a DARPin selected against the epithelial cell adhesion molecule (EpCAM) with excellent properties for tumor targeting as an example. We used these doubly modified molecules to measure binding kinetics on tumor cells and found that PEGylation has no effect on dissociation rate, but slightly decreases the association rate and the maximal number of cell-bound DARPins, fully consistent with our previous model of PEG action obtained <i>in vitro</i>. Our data demonstrate the benefit of click chemistry for site-specific modification of binding proteins like DARPins to conveniently add several functional moieties simultaneously for various biomedical applications

Novel Prodrug-Like Fusion Toxin with Protease-Sensitive Bioorthogonal PEGylation for Tumor Targeting

Highly potent biotoxins like Pseudomonas exotoxin A (ETA) are attractive payloads for tumor targeting. However, despite replacement of the natural cell-binding domain of ETA by tumor-selective antibodies or alternative binding proteins like designed ankyrin repeat proteins (DARPins) the therapeutic window of such fusion toxins is still limited by target-independent cellular uptake, resulting in toxicity in normal tissues. Furthermore, the strong immunogenicity of the bacterial toxin precludes repeated administration in most patients. Site-specific modification to convert ETA into a prodrug-like toxin which is reactivated specifically in the tumor, and at the same time has a longer circulation half-life and is less immunogenic, is therefore appealing. To engineer a prodrug-like fusion toxin consisting of the anti-EpCAM DARPin Ec1 and a domain I-deleted variant of ETA (ETA″), we used strain-promoted azide alkyne cycloaddition for bioorthogonal conjugation of linear or branched polyethylene glycol (PEG) polymers at defined positions within the toxin moiety. Reversibility of the shielding was provided by a designed peptide linker containing the cleavage site for the rhinovirus 3C model protease. We identified two distinct sites, one within the catalytic domain and one close to the C-terminal KDEL sequence of Ec1-ETA″, simultaneous PEGylation of which resulted in up to 1000-fold lower cytotoxicity in EpCAM-positive tumor cells. Importantly, the potency of the fusion toxin was fully restored by proteolytic unveiling. Upon systemic administration in mice, PEGylated Ec1-ETA″ was much better tolerated than Ec1-ETA″; it showed a longer circulation half-life and an almost 10-fold increased area under the curve (AUC). Our strategy of engineering prodrug-like fusion toxins by bioorthogonal veiling opens new possibilities for targeting tumors with more specificity and efficacy