Convertible Bonds: Default Risk and Uncertain Volatility

Within a default intensity approach we discuss the optimal exercise of the callable and convertible bonds. Pricing bounds for convertible bonds are derived in an uncertain volatility model, i.e. when the volatility of the stock price process lies between two extreme values.Convertible bond, game option, uncertain volatility, interest rate risk

Convertible Bonds: Risks and Optimal Strategies

Within the structural approach for credit risk models we discuss the optimal exercise of the callable and convertible bonds. The Vasi˘cekâmodel is applied to incorporate interest rate risk into the firmâs value process which follows a geometric Brownian motion. Finally, we derive pricing bounds for convertible bonds in an uncertain volatility model, i.e. when the volatility of the firm value process lies between two extreme values.Convertible bond, game option, uncertain volatility, interest rate risk

Valuation of Convertible Bonds

Convertible bonds are hybrid financial instruments with complex features. They have characteristics of both debts and equities, and usually several options are embedded in this kind of contracts. The optimality of the conversion decision depends on equity price, interest rate and default probability of the issuer. The decision making can be further complicated by the fact that most convertible bonds have call provisions allowing the bond issuer to call back the bond at a predetermined call price. In this thesis, we first adopt a structural approach where the Vasicek-model is applied to incorporate interest rate risk into the firm's value process which follows a geometric Brownian motion. Default is triggered when the firm's value hits a lower boundary. The complex nature of the firm's capital structure and information asymmetry may make it hard to model the firm's value and the capital structure. In this case, reduced-form models are applied for the study of convertible bonds. We adopt a parsimonious, intensity-based default model, in which the default intensity is modeled as a function of the pre-default stock price. We first analyze the contract features of the convertible bonds and show that callable and convertible bonds can be decomposed into a straight bond and a game option component. Then the no-arbitrage prices of the European- and American-style callable and convertible bonds are derived. In American-style contracts, the focus is on the analysis of the strategic optimal behavior. The bondholder and issuer choose their stopping times to maximize or minimize the expected payoff respectively. For the bondholder it is optimal to select the stopping time which maximizes the expected payoff given the minimizing strategy of the issuer, while the issuer will choose the stopping time that minimizes the expected payoff given the maximizing strategy of the bondholder. The no-arbitrage price can be approximated numerically by means of backward induction. In the structural model, the recursion is carried out alongside a recombining binomial tree. Whereas in the reduced-form approach, the optimization problem is formulated and solved with the help of the theory of doubly reflected backward stochastic differential equations. In practice, it is often a difficult problem to calibrate a given model to the available data. Determining the volatility of the firm's value process or stock price process is not a trivial problem. We therefore assume that the volatility of the firm's value process/stock price process lies between two extreme values, and combine it with the results on game option in incomplete market to derive certain pricing bounds for callable and convertible bonds. The maximizing strategy of the bondholder and the choice of the most pessimistic pricing measure from his perspective determine the lower bound of the no-arbitrage price. Whereas the minimizing strategy of the issuer and the most pessimistic expectation from his aspect construct the upper bound of the no-arbitrage price. Numerically, to make the computation tractable a constant interest rate is assumed. The pricing bounds can be calculated with recursion alongside a recombining trinomial tree or with the finite-difference method

Bioresponsive functional nanogels as an emerging platform for cancer therapy

Introduction: Bioresponsive nanogels with a crosslinked three-dimensional structure and an aqueous environment that undergo physical or chemical changes including swelling and dissociation in response to biological signals such as mild acidity, hyperthermia, enzymes, reducing agents, reactive oxygen species (ROS), and adenosine-5ʹ-triphosphate (ATP) present in tumor microenvironments or inside cancer cells have emerged as an appealing platform for targeted drug delivery and cancer therapy. Areas covered: This review highlights recent designs and development of bioresponsive nanogels for facile loading and triggered release of chemotherapeutics and biotherapeutics. The in vitro and in vivo antitumor performances of drug-loaded nanogels are discussed. Expert opinion: Bioresponsive nanogels with an excellent stability and safety profile as well as fast response to biological signals are unique systems that mediate efficient and site-specific delivery of anticancer drugs, in particular macromolecular drugs like proteins, siRNA and DNA, leading to significantly enhanced tumor therapy compared with the non-responsive counterparts. Future research has to be directed to the development of simple, tumor-targeted and bioresponsive multifunctional nanogels, which can be either constructed from natural polymers with intrinsic targeting ability or functionalized with targeting ligands. We anticipate that rationally designed nanotherapeutics based on bioresponsive nanogels will become available for future clinical cancer treatment. Abbreviations: AIE, aggregation-induced emission; ATP, adenosine-5ʹ-triphosphate; ATRP, atom transfer radical polymerization; BSA, bovine serum albumin; CBA, cystamine bisacrylamide; CC, Cytochrome C; CDDP, cisplatin; CT, computed tomography; DC, dendritic cell; DiI, 1,1ʹ-dioctadecyl-3,3,3ʹ,3ʹ-tetramethylindocarbocyanine perchlorate; DOX, doxorubicin; dPG, dendritic polyglycerol; DTT, dithiothreitol; EAMA, 2-(N,N-diethylamino)ethyl methacrylate; EPR, enhanced permeability and retention; GrB, granzyme B; GSH, glutathione tripeptide; HA, hyaluronic acid; HAase, hyaluronidases; HCPT, 10-Hydroxycamptothecin; HEP, heparin; HPMC, hydroxypropylmethylcellulose; LBL, layer-by-layer; MTX, methotrexate; NCA, N-carboxyanhydride; OVA, ovalbumin; PAH, poly(allyl amine hydrochloride); PBA, phenylboronic acid; PCL, polycaprolactone; PDEAEMA, poly(2-diethylaminoethyl methacrylate); PDGF, platelet derived growth factor; PDPA, poly(2-(diisopropylamino)ethyl methacrylate); PDS, pyridyldisulfide; PEG, poly(ethylene glycol); PEGMA, polyethyleneglycol methacrylate; PEI, polyethyleneimine; PHEA, poly(hydroxyethyl acrylate); PHEMA, poly(2-(hydroxyethyl) methacrylate; PNIPAM, poly(N-isopropylacrylamide); PMAA, poly(methacrylic acid); PPDSMA, poly(2-(pyridyldisulfide)ethyl methacrylate); PTX, paclitaxel; PVA, poly(vinyl alcohol); QD, quantum dot; RAFT, reversible addition-fragmentation chain transfer; RGD, Arg-Gly-Asp peptide; ROP, ring-opening polymerization; ROS, reactive oxygen species; TMZ, temozolomide; TRAIL, tumor necrosis factor-related apoptosis inducing ligand; VEGF, vascular endothelial growth factor

Folated pH-degradable nanogels for the simultaneous delivery of docetaxel and an IDO1-inhibitor in enhancing cancer chemo-immunotherapy

Combining chemotherapy and immunotherapy has been considered as an attractive approach to improve cancer therapy. Here we prepared folated PVA-based nanogels for the simultaneous delivery of docetaxel (DTX) and the indoleamine 2,3-dioxygenase 1 (IDO1) inhibitor NLG919 (N9) for enhancing cancer chemo-immunotherapy. FDA-approved poly(vinyl alcohol) (PVA) with good biocompatibility was modified with vinyl ether acrylate (VEA) groups for UV-crosslinking and acidic degradation. Carboxyl groups were introduced via modification with succinic anhydride for improved drug loading and folic acid (FA) ligands were incorporated for tumor targeting. UV-crosslinked folated PVA nanogels were efficiently taken up by tumor cells followed by endo/lysosomal pH-triggered intracellular drug release, which induced significant cytotoxicity towards 4T1 breast cancer cells in vitro. DTX and N9 co-loaded PVA nanogels exhibited a much higher antitumor efficiency in 4T1 mouse breast cancer models in vivo as compared to the free drug controls. The drug-laden nanogels not only directly killed the tumor cells by DTX, but also induced immunogenic cell death (ICD) promoting intratumoral accumulation of cytotoxic T lymphocytes, and further combining with N9 elevated the intratumoral infiltration of CD8+ T cells and NK cells and inhibited the infiltration of MDSCs, downregulating IDO1-mediated immunosuppression